January 13, 2020 Developing Next-Generation Epigenetic Treatments for Cancer Patients Jigar Raythatha, CEO J.P. Morgan Healthcare Conference Exhibit 99.1

This presentation and discussion contain “forward-looking statements” within the meaning of the Private Securities Litigation Reform Act of 1995 that involve substantial risks and uncertainties, including statements regarding the implications of preliminary or interim clinical data, the development status of the Company’s product candidates, and the Company’s plans for future data presentations. All statements, other than statements of historical facts, contained in this press release, including statements regarding the Company’s strategy, future operations, future financial position, prospects, plans and objectives of management, are forward-looking statements. The words “anticipate,” “believe,” “continue,” “could,” “estimate,” “expect,” “intend,” “may,” “plan,” “potential,” “predict,” “project,” “should,” “target,” “will,” “would” and similar expressions are intended to identify forward-looking statements, although not all forward-looking statements contain these identifying words. Any forward-looking statements are based on management’s current expectations of future events and are subject to a number of risks and uncertainties that could cause actual results to differ materially and adversely from those set forth in, or implied by, such forward-looking statements. These risks and uncertainties include, but are not limited to, risks associated with Constellation’s ability to: obtain and maintain necessary approvals from the FDA and other regulatory authorities; continue to advance its product candidates in clinical trials; whether preliminary or interim data from a clinical trial will be predictive of the final results of the trial; replicate in later clinical trials positive results found in preclinical studies and early-stage clinical trials of CPI-0610, CPI-1205, and CPI-0209; advance the development of its product candidates under the timelines it anticipates, or at all, in current and future clinical trials; obtain, maintain, or protect intellectual property rights related to its product candidates; manage expenses; and raise the substantial additional capital needed to achieve its business objectives. For a discussion of other risks and uncertainties, any of which could cause the Company’s actual results to differ from those contained in the forward-looking statements, see the “Risk Factors” section, as well as discussions of potential risks, uncertainties and other important factors, in the Company’s most recent filings with the Securities and Exchange Commission, including the Company’s Quarterly Report on Form 10-Q for the quarter ended September 30, 2019. In addition, the forward-looking statements included in this press release represent the Company’s views as of the date hereof and should not be relied upon as representing the Company’s views as of any date subsequent to the date hereof. The Company anticipates that subsequent events and developments will cause the Company’s views to change. However, while the Company may elect to update these forward-looking statements at some point in the future, the Company specifically disclaims any obligation to do so. CPI-1205, CPI-0610, CPI-0209, and other product candidates are investigational in nature and have not yet been approved by the FDA or other regulatory authorities. Forward-Looking Statements

Constellation Highlights Multiple wholly owned clinical programs: CPI-0610 (BET) and CPI-1205 and CPI-0209 (EZH2) CPI-0610 has potential to transform standard of care in 1L myelofibrosis as well as provide improved quality of life and disease-modifying benefits in 2L myelofibrosis CPI-1205 has been well tolerated and active in clinical studies in combination with ARS inhibitors in prostate cancer CPI-0209 expands the potential of our EZH2 franchise through comprehensive target engagement over time Robust discovery platform fuels the pipeline

Product Candidates Indications Preclinical Phase 1 Phase 2 Phase 3 Next Steps BET Inhibitor CPI-0610 2L Myelofibrosis 1L Myelofibrosis MANIFEST update in mid-2020 Phase 3 start in mid-2020 Program update in late 2020 EZH2 Franchise CPI-1205 2L mCRPC* ProSTAR update in mid-2020 CPI-0209 (2nd Generation) Solid Tumors Program update in 2H20 Preclinical Tumor Targeted (Undisclosed) Solid Tumors/ Heme Malignancies Tumor Microenvironment Targeted (Undisclosed) Solid Tumors Multiple Near-Term Opportunities for Success * Metastatic castration-resistant prostate cancer ProSTAR Trial MANIFEST Trial

CPI-0610

Reduce Inflammation and Suppress Cells in the Bone Marrow that Drive MF (Megakaryocytes) Mechanism of Potential Disease Modification in Myelofibrosis STAT STAT BETs P P

CPI-0610 Is a Potential Best-in-Class BET Inhibitor and a Potential Disease-Modifying Therapy for MF *CR also achieved at lower dose of 48mg QD capsule **Ability to titrate up to 225 mg #Source – Forero-Torres et al. (2017) – Poster at American Society for Hematology 2017 Annual Meeting ^Sources – Amorin et al. (2016) Lancet Haematology, Volume 3, Issue 4 196-204 Selected BET Inhibitors with Published Phase 1 Lymphoma Data 300 200 100 0 Dose – mg (once daily) Maximum Tolerated Dose CPI-0610 INCB057643# OTX-015^ MK-8628^ Active Lymphoma Dose/MF Ph2 Dose** Active Doses Lowest Active Dose* Potent and selective inhibitor of BET proteins Treated > 250 patients in trials of various hematologic malignancies Preliminary clinical activity observed: Potentially disease modifying in MF (Phase 2) Lymphoma – e.g., ABC-DLBCL (Phase 1) Signals of potentially differentiated safety profile Phase 1 data suggest that thrombocytopenia (DLT) is dose dependent, reversible and non-cumulative Activity seen at range of doses below the MTD

Vision: Transform Standard of Care in MF with a Differentiated Therapeutic Option Myelofibrosis Patient Journey Disease Progression Symptomatic MF Fibrotic Bone Marrow 1L: Start JAKi Fibrotic Bone Marrow 2L: Continue on JAKi Fibrotic Bone Marrow 2L: Stop JAKi Fibrotic Bone Marrow CPI-0610 Add-On CPI-0610 Monotherapy CPI-0610 + Rux Combo

TD = Transfusion Dependent Cohorts 1A/1B and Cohorts 2A/2B will apply a Simon-2 stage design MANIFEST Study Design Overview Cohort 1A: TD n = up to 16 patients Cohort 1B: Non-TD n = up to 25 patients CPI-0610 Mono Cohort 2A: TD n = up to 16 patients Cohort 2B: Non-TD n = up to 25 patients CPI-0610 + Ruxolitinib Study Population Treatment Arm/Cohort Arm 3: JAKi Naive n = up to 43 patients CPI-0610 + Ruxolitinib Second line: No longer on ruxolitinib Refractory or intolerant or ineligible Second line: “Add on” to ruxolitinib Sub-optimal response or MF progression First line: No prior JAK inhibitor use Recently expanded Cohort 2A to up to 60 patients Recently expanded to up to 101 patients Randomized Phase 3 planned to initiate in 2020

Data Cutoff October 17, 2019 Arm 3 (CPI-0610 + Ruxolitinib): Spleen Volume Reduction at 12 Weeks % Spleen Volume Reduction at 12 Weeks (n=15)1 80% (12/15) SVR35 response rate at 12 weeks Median % change at 12 weeks: -49.7% (range: -80.8%, -17.0%) These 15 patients represent a high-risk population 87%1 are DIPSS ≥Int-2 80%1 have Hgb < 10g/dL 53%1 are HMR positive Median ruxolitinib dose2: 10mg BID 1 Evaluable patients: Patients received at least 12 weeks of treatment, have baseline and post-baseline SVR assessment at 12 weeks 2 Ruxolitinib dose for longest duration during 12 weeks SVR35 response: ≥35% spleen volume reduction TSS50 response: ≥50% improvement in Total Symptom Score (Myelofibrosis Symptom Assessment Form v.4) HMR: patient with ≥ 1 High Molecular Risk mutation. Hgb: hemoglobin. DIPSS: Dynamic International Prognostic Scoring System Expect to present 24-week data on 20-30 patients mid-2020

1 Evaluable patients: Baseline and 12-week data available. One patient TSS non-evaluable due to missing baseline. TSS50 Response: ≥50% improvement in Total Symptom Score (Myelofibrosis Symptom Assessment Form v4) SVR35 Response: ≥35% spleen volume reduction HMR: Patients with ≥ 1 High Molecular Risk mutation ; Hgb: Hemoglobin Data Cutoff October 17, 2019 Arm 3 (CPI-0610 + Ruxolitinib): Total Symptom Improvement at 12 Weeks % TSS Improvement at 12 Weeks (n=14)1 71% (10/14) patients had TSS50 response Median % change at 12 weeks: 60.3% (range: -100%, 90%) Patient with dose interruption due to AE unrelated to CPI-0610 had 41.7% reduction in TSS at assessment (at Week 6) prior to dose interruption

Data Cutoff October 17, 2019 Arm 3 (CPI-0610 + Ruxolitinib): Most Common Adverse Events (AE) CPI-0610 in combination with ruxolitinib in Arm 3 patients was generally well tolerated No AEs led to study discontinuation 3 patients had ≥ Grade 3 anemia 1 patient had Grade 4 thrombocytopenia Most common non-hematologic AEs were primarily Grade 1/2 – diarrhea, nausea, dizziness, and muscle spasms Rates of infections were low, and no new or unexpected infections were observed Adverse Events1 All Grade N = 302 n (%) ≥3 Grade N = 302 n (%) Hematological Events Anemia 6 (20.0%) 3 (10.0%) Thrombocytopenia3 5 (16.7%) 1 (3.3%)4 Non-Hematological Events Gastrointestinal Events Diarrhea 8 (26.7%) 0 Nausea 6 (20.0%) 0 Constipation 3 (10.0%) 0 Mouth ulceration 3 (10.0%) 0 Other Non-Hematological Events Dizziness 4 (13.3%) 0 Muscle spasms 4 (13.3%) 0 Dyspnea 3 (10.0%) 1 (3.3%)4 1 AEs of all grade that occurred in ≥10% of patients 2 Safety evaluable population: Received Cycle 1 Day 1 treatment (N=30) 3 Includes AE Platelet count decrease. 4 AE of special interest although occurred in <10% of patients

Efficacy Results at 24 Weeks, Data Cutoff October 17, 2019 CPI-0610 Monotherapy or Add-on to Ruxolitinib in R/R/I* MF Patients % Spleen Volume Change at 24 Weeks (n=34)1 Median change at 24 weeks: -18% SVR35 response rate at 24 weeks in Cohort 2A: 25% (3/12) Median change at 24 weeks in Cohort 2A: -24.9% 1 Evaluable patients: Patients received at least 24 weeks of treatment, have baseline and 24-week post-baseline assessment available SVR35 response: ≥35% Reduction in Spleen Volume by MRI/CT + Patient with ≥ 1 HMR mutation ↑ TDà TI conversion TD = Transfusion dependent, defined as receiving an average of ≥ 2 RBC transfusions per month during the 12 weeks prior to enrollment TI = Transfusion independent, defined as absence of RBC transfusions over any consecutive 12-week period *Relapsed or refractory or intolerant

Efficacy Results at 24 Weeks, Data Cutoff October 17, 2019 CPI-0610 Monotherapy or Add-on to Ruxolitinib in R/R/I* MF Patients Median change at 24 weeks: -47% TSS50 response rate at 24 weeks in Cohort 2A: 54% (7/13) Median change in Cohort 2A: -58.8% % TSS Change at 24 Weeks (n=32)1 1 Evaluable patients: Patients received at least 24 weeks of treatment, have baseline and 24-week post-baseline assessment available TSS50 response: ≥50% Reduction in Total Symptom Score per MFSAF v4.0 + Patient with ≥ 1 HMR mutation ↑ TDà TI conversion TD = Transfusion dependent, defined as receiving an average of ≥ 2 RBC transfusions per month during the 12 weeks prior to enrollment TI = Transfusion independent, defined as absence of RBC transfusions over any consecutive 12-week period *Relapsed or refractory or intolerant

Cohort 2B: CPI-0610 + Ruxolitinib (n=15)1 1Hemoglobin change in evaluable population: Received treatment for ≥12 weeks, without any transfusion 2The increases in hemoglobin from baseline. Mean+/-SEM. 3Bone marrow evaluable population: Baseline and at least one post-baseline bone marrow biopsy at or after 24 weeks available Data Cutoff October 17, 2019 Hemoglobin and Bone Marrow Fibrosis Improvement Cohort 1B: CPI-0610 Monotherapy (n=11)1 12 of 32 (38%) patients3 had at least one grade improvement in bone marrow fibrosis 10 of 12 (83%) improvements occurred within the first six months of treatment 55% (6/11) patients had ≥1.5 g/dL increase in hemoglobin2 13% (2/15) patients had ≥1.5 g/dL increase in hemoglobin2

1Adverse events of all grade that occurred in ≥10% of patients in Arm1 & 2 combined 2Safety evaluable population from Arm 1 and 2: Received Cycle 1 Day 1 treatment (N=90) 3Includes AE platelet count decrease 4Although all grade occurred in <10% of patients, listed because ≥Grade 3 occurred in ≥5% of patients Data Cutoff October 17, 2019 Arms 1 & 2: Most Common Adverse Events (AEs) CPI-0610 either as monotherapy or in combination with ruxolitinib in MF patients was generally safe and well tolerated Most common hematologic AE – thrombocytopenia3 9 patients showed ≥ Grade 3 thrombocytopenia, all are non-serious Arm 1: two patients (5.6%), one required dose reduction Arm 2: seven patients (12.9%), one required dose interruption and two required dose reduction Most common non-hematologic AEs were primarily grade 1 or 2 – diarrhea, nausea, cough, fatigue, vomiting, and upper respiratory tract infection 3 out of 90 (3.3%) patients reported Grade 5 AEs Acute kidney injury Traumatic subdural hematoma (fall due to tripping) Brain stem hemorrhage (no concomitant thrombocytopenia) Adverse Events1 All Grade N = 90 n (%)2 ≥3 Grade N = 90 n (%)2 Hematological Events Thrombocytopenia3 21 (23.3) 9 (10.0) Anemia4 8 (8.9) 6 (6.7) Non-Hematological Events Gastrointestinal Events Diarrhea 29 (32.2) 4 (4.4) Nausea 20 (22.2) 1 (1.1) Vomiting 13 (14.4) 1 (1.1) Constipation 10 (11.1) 1 (1.1) Abdominal distension 9 (10.0) 0 Other Non-Hematological Events     Cough 15 (16.7) 0 Fatigue 13 (14.4) 3 (3.3) Upper respiratory tract infection 13 (14.4) 0 Headache 10 (11.1) 1 (1.1) Edema peripheral 10 (11.1) 0 Pain in extremity 10 (11.1) 0 Decreased appetite 9 (10.0) 1 (1.1) Dysgeusia 9 (10.0) 1 (1.1) Contusion 9 (10.0) 0

^COMFORT-1: A Double-Blind, Placebo-Controlled Trial of Ruxolitinib for Myelofibrosis Verstovsek, S., et al; N Engl J Med 2012;366:799-807. *SIMPLIFY-1: A Phase III Randomized Trial of Momelotinib Versus Ruxolitinib in Janus Kinase Inhibitor-Naïve Patients With Myelofibrosis. Mesa, R., et al. J Clin Oncol 2017: 35(34):3844-3850. Current Benchmarks for Standard of Care in 1L JAKi-Naive Comfort-2 data available at right, but not used because it shows best response rather than 24 weeks Change in Spleen Volume from Baseline (%) Ruxolitinib Spleen Volume Response (SVR%) 100% 80% 60% 40% 20% 0% -20% -40% -60% 41.9% SVR35 29% SVR35 ^ * SIMPLIFY-1* COMFORT-1^

Proposed Global Pivotal Phase 3 Clinical Trial Study Population Treatment Arm/Cohort Endpoints Design/Size Placebo + Ruxolitinib CPI-0610 + Ruxolitinib JAK-inhibitor-naïve primary MF or post-ET/PV MF patients with: Advanced MF requiring therapy Palpable spleen Symptomatic Double-Blind Randomization Primary: SVR at 24 weeks Key Secondary: TSS by MFSAF v4.0* at 24 weeks Expected to Begin Mid-2020 Also exploring novel endpoints (e.g., conversion to transfusion independence in transfusion-dependent patients) in relapsed/refractory patients as alternative registrational strategy *MFSAF v4.0 = Myelofibrosis Symptom Assessment Form version 4.0

CPI-0610 Patient Opportunity ~40,000 Diagnosed Myelofibrosis Patients Worldwide (4-6/100,000) Low Risk/ Asymptomatic Intermediate- and High Risk CPI-0610 Patient Opportunity Don’t Start JAKi Start/Continue JAKi Stop JAKi JAKi Patient Population Add CPI-0610 to JAKi Therapy Start CPI-0610/JAKi Stop JAKi Start CPI-0610 Potential for CPI-0610 to Become Part of New Standard of Care and Expand the MF Opportunity

EZH2 Franchise

Franchise Approach to Address the Breadth of EZH2 Biology Polycomb Repressive Complex 2 … Methylates Histone H3 at Lysine 27 EZH2 SUPPRESSED TRANSCRIPTION Synergy w/ Oncogenic Drivers Tumor Immunity Drug Resistance Synthetic Lethality Activating Mutations First-Generation EZH2i – CPI-1205 Potent Typical enzyme inhibitor kinetics Partial target coverage over time Best for hypersensitive contexts Second-Generation EZH2i – CPI-0209 Even more potent Durable inhibition of EZH2 Comprehensive target coverage over time Expands beyond 1st gen contexts

*Bradley, WD, et al., ”EZH2 Inhibition as an Effective Treatment for Metastatic Castration-Resistant Prostate Cancer,” presentation at 2018 EORTC/NCI/AACR meeting EZH2 Synergy with Androgen Receptor Signaling (ARS) CPI-1205 Intensifies Gene Expression Effects of Enzalutamide in Prostate Cancer Cells* CPI-1205 is Active as Monotherapy and Synergistic with Enzalutamide in Killing Prostate Cancer Cells Enzalu- tamide CPI- 1205 Combo Theoretical concentration of each agent required to kill 90% of cancer cells if no synergistic activity Actual concentration of each agent required to kill 90% of cancer cells when combined Synergy

Note: In ProSTAR, abiraterone is dosed in combination with prednisone * Primary endpoint: maximum tolerated dose, recommended Phase 2 dose ** Primary endpoint: Response rate: PSA reduction, CTC reduction, objective response rate (ORR) *** Primary endpoint: ORR Phase 2 Initiated ProSTAR Trial Design Enzalutamide + CPI-1205 (Progressed on Abiraterone) n ~ 35 Enzalutamide Alone (Progressed on Abiraterone) n ~ 35 vs. CPI-1205 + Enzalutamide* (Prior Abiraterone Progression) Abiraterone + CPI-1205 (Prior Enzalutamide Progression) Phase 1b – Advanced mCRPC Phase 2 – 2L mCRPC Patients Only CPI-1205 + Abiraterone (Progressed on Enzalutamide) n ~ 30 Initiated Initiated Initiated Testing Biomarkers for Patient Enrichment Enzalutamide + CPI-1205 (Progressed on Abiraterone) n ~ 35 Enzalutamide Alone (Progressed on Abiraterone) n ~ 35 CPI-1205 + Abiraterone (Progressed on Enzalutamide) n ~ 30 CPI-1205 + Abiraterone* (Prior Enzalutamide Progression) CPI-1205 + Enzalutamide** (Progressed on Abiraterone) n ~ 35 Enzalutamide Alone** (Progressed on Abiraterone) n ~ 35 CPI-1205 + Abiraterone** (Progressed on Enzalutamide) n ~ 30 Enzalutamide + CPI-1205*** (Progressed on Abiraterone, Enzalutamide, and Chemotherapy)

Lymphoma Xenograft – Mutated EZH2 Model Once-Daily Treatment Resulted in Rapid and Durable Tumor Regression CPI-0209: Second-Generation EZH2 Inhibitor CPI-0209 May Provide More Comprehensive EZH2 Coverage, Expanding Addressable Populations Cessation of treatment Vehicle CPI-0209, 25 mg/kg oral, once daily Bladder Cancer – Mutated ARID1A Model Tumor Volume (mm3) Other EZH2 Inhibitors 75 mg/kg oral once daily CPI-0209 75 mg/kg oral once daily Vehicle Days of Treatment

Design of Phase 1/2 Clinical Trial of CPI-0209 Phase 1 Dose Escalation: CPI-0209 Monotherapy Phase 2 Expansion at RP2D*: CPI-0209 Monotherapy Initiated Initiated Initiated Initiated Advanced, Relapsed Solid Tumors Primary endpoints: Safety, Recommended Phase 2 Dose (RP2D) Primary endpoints: Safety, RP2D Biomarker-Defined Solid Tumor Populations Clear-Cell Ovarian Carcinoma Biomarker-Defined Solid Tumor Populations Resistant to Standard of Care Primary endpoint: Objective Response Rate Primary endpoint: Objective Response Rate Advanced, Relapsed Solid Tumors Phase 1 Dose Escalation*: CPI-0209 Combo with Standard of Care Phase 2 Expansion at RP2D: CPI-0209 Combo with Standard of Care * Expected to be conducted simultaneously

2H 2020 Potential Value Creation Catalysts 1H 2020 CPI-0610 – Mid-year program update from MANIFEST CPI-1205 – Mid-year program update from ProSTAR CPI-0610 – Planned initiation of Phase 3 clinical trial in mid-2020 CPI-0209 – Program update and initiation of Phase 2 clinical trial CPI-0610 – Program update by end of year

Taking Constellation to the Next Level 2019: Generated POC for CPI-0610 Raised capital to support pivotal Phase 3 clinical trial of CPI-0610 Expanded clinical portfolio with CPI-0209 Built out capabilities Year of Data 2020: Begin Phase 3 clinical trial for CPI-0610 in 1L MF Build initial commercial infrastructure Determine next steps for CPI-1205 program Establish RP2D for CPI-0209 Advance preclinical pipeline Build a Fully Integrated Company