Inclusion Criteria:

• Study entry
• 1. Subject must be able to understand the purpose of the study and be willing to participate and provide written consent
• 2. Recipient of a primary heart transplant (heart transplant only)
• 3. Epstein-Barr Virus (EBV) seropositive
• 4. Agreement to use contraception; according to the Food and Drug Administration (FDA) Office of Women's Health (http://www.fda.gov/birthcontrol), there are a number of birth control methods that are more than 80% effective. Female participants of child-bearing potential must consult with their physician and determine the most suitable method(s) from this list to be used for the duration of the study
• 5. In the absence of a contraindication, vaccinations must be up to date per the Division of Allergy, Immunology, and Transplantation (DAIT) Vaccination Guidance for Patients in Transplant Trials (Refer to the Manual of Procedures)
• 6. Mechanical support or investigational drug trials where the intervention ends at the time of transplantation are permitted.
• Randomization
• 1. Recipient of a primary heart transplant
• 2. No desensitization therapy prior to transplant
• 3. Negative crossmatch actual or virtual, on the most recent sera as determined by the participating study center
• 4. Female subjects of childbearing potential must have a negative pregnancy test (serum or urine) prior to randomization
• 5. Agreement to use contraception; according to the FDA Office of Women's Health (http://www.fda.gov/birthcontrol), there are a number of birth control methods that are more than 80% effective. Female participants of child-bearing potential must consult with their physician and determine the most suitable method(s) from this list to be used for the duration of the study. Those who choose oral contraception must agree to use a second form of contraception after administration of study drug for a period of 1 year after the last dose of study drug
• 6. Estimated Glomerular Filtration Rate (eGFR) (Chronic Kidney Disease Epidemiology Collaboration equation (CKD-epi)) \>30ml/min/1.73m\^2 and \<100ml/min/1.73m\^2

Exclusion Criteria:

• Study entry
• 1. Candidate for multiple solid organ or tissue transplants
• 2. Prior history of any organ, tissue, or cellular transplant
• 3. Currently breast-feeding a child or plans to become pregnant during the timeframe of the study follow up period
• 4. History of severe allergic and/or anaphylactic reactions to humanized or murine monoclonal antibodies
• 5. Known hypersensitivity to NULOIX (belatacept) or ORENCIA (Abatacept)
• 6. Previous treatment with NULOIX (belatacept) or ORENCIA (Abatacept)
• 7. Epstein Barr Virus (EBV) seronegative or indeterminant
• 8. Human Immunodeficiency Virus (HIV) positive
• 9. Hepatitis B surface antigen positive
• 10. Hepatitis B core antibody positive
• 11. Hepatitis C virus antibody (HCV Ab+) and hepatitis C virus (HCV) Polymerase Chain Reaction (PCR) positive patients
• 12. Patients with a previous history of active Tuberculosis (TB)
• 13. Subjects must be tested for latent TB infection (LTBI) within a year prior to transplant. Testing should be conducted using either a PPD or Interferon-gamma release assay (i.e., QuantiFERON-TB, T-SPOT.TB). Patients with a positive test for latent TB infection (LTBI) must have completed appropriate therapy for LTBI (https://www.cdc.gov/tb/topic/treatment/ltbi.htm). A subject is considered eligible only if they have a negative test for LTBI within one year prior to transplant OR if they have completed appropriate LTBI therapy within one year prior to transplant
• 14. Positive serology for T. cruzi or known/suspected history of Chagas disease
• 15. Findings on pre-transplant or pre-randomization chest x-ray suggestive of fungal infection.
• Participants with a normal chest x-ray but positive serologies for coccidiomycosis, histoplasmosis, or blastomycosis, who have previously been fully treated, will be permitted to participate but require prophylaxis as further outlined in Section 7
• 16. Known active current viral, fungal, mycobacterial or other infections (including, but not limited to atypical mycobacterial disease and herpes zoster), not including drive line infections
• 17. White blood cell (WBC) count \<3.0 or an absolute neutrophil count (ANC) of less than 1500 cells/mm3 on \>=2 occasions at any time prior to enrollment
• 18. History of central nervous system (CNS) infection
• 19. History of active inflammatory bowel disease, chronic diarrhea, or malabsorption
• 20. History of malignancy, per discretion of oncology consult and study oversight team, will be permitted to participate
• 21. History of AL amyloidosis
• 22. Patients who are administered or intended to be administered induction therapy (cytolytic agents such as anti-thymocyte globulin or anti-IL2R therapies such as basiliximab) in the immediate peri- transplant period
• 23. Patients who i) have undergone desensitization, ii) are undergoing or are planned to undergo desensitization, or iii) are intended to receive therapeutic interventions that are used for the purpose of desensitization prior to transplant
• 24. Pretransplant Calculated Panel Reactive Antibody (cPRA) calculated by Single Antigen Bead (SAB) testing \> 25%
• 25. The use of immunosuppressive biologics within 3 months prior to transplant is not permitted. Non- immunosuppressive biologics such as proprotein convertase subtilisin/kexin type 9 (PCSK9) inhibitors must be stopped at the time of transplant
• 26. Patients for whom there is an intent to administer biologics other than those indicated by protocol during the study period
• 27. The intended use of high dose (\>= 2g/kg) intravenous immunoglobulin before or at the time of transplant or before study drug administration
• 28. A personal history of severe hypogammaglobulinemia (\<300mg/dL)
• 29. Intent to give the patient a live vaccine within 30 days prior to randomization
• 30. Use or intended use of other investigational drugs after transplant
• 31. Past or current medical problems or findings from physical examination or laboratory testing that are not listed above, which, in the opinion of the investigator, may pose additional risks from participation in the study, may interfere with the potential participant's ability to comply with study requirements or that may impact the quality or interpretation of the data obtained from the study
• Randomization
• 1. Recipient of multiple solid organ or tissue transplants
• 2. Prior history of any organ, tissue, or cellular transplant
• 3. Currently breast-feeding a child or plans to become pregnant during the timeframe of the study follow up period
• 4. History of severe allergic anaphylactic reactions to humanized or murine monoclonal antibodies
• 5. Known hypersensitivity to Belatacept (NULOJIX) or Abatacept (ORENCIA)
• 6. Previous treatment with Belatacept (NULOJIX) or Abatacept (ORENCIA)
• 7. Epstein Barr Virus (EBV) seronegative or indeterminant
• 8. HIV positive patient
• 9. Hepatitis B surface antigen positive patient
• 10. Hepatitis B core antibody positive patient
• 11. Hepatitis B negative transplant recipient that received a transplant from a Hepatitis B core antibody positive donor
• 12. Hepatitis C virus antibody (HCV Ab+) and HCV PCR positive patients
• 13. Recipient of allograft from a hepatitis C virus nucleic acid test (NAT) positive donor
• 14. Patients with a previous history of active Tuberculosis (TB)
• 15. Subjects must be tested for latent TB infection (LTBI) within a year prior to transplant. Testing should be conducted using either a PPD or Interferon-gamma release assay (i.e., QuantiFERON-TB, T-SPOT.TB). Patients with a positive test for latent TB infection (LTBI) must complete appropriate therapy for LTBI (https://www.cdc.gov/tb/topic/treatment/ltbi.htm). A subject is considered eligible only if they have a negative test for LTBI within one year prior to transplant OR if they have completed appropriate LTBI therapy within one year prior to transplant
• 16. Positive serology for T. cruzi or known/suspected history of Chagas disease
• 17. Findings on pre-transplant or pre-randomization chest x-ray suggestive of fungal infection.
• Participants with a normal chest x-ray but positive serologies for coccidiomycosis, histoplasmosis, or blastomycosis, who have previously been fully treated, will be permitted to participate but require prophylaxis as further outlined in Section 7
• 18. Known active current viral, fungal, mycobacterial or other infections (including, but not limited to atypical mycobacterial disease and herpes zoster), not including drive line infections
• 19. White blood cell (WBC) count \<3.0 or an absolute neutrophil count (ANC) of less than 1500 cells/mm3 on \>=2 occasions at any time prior to randomization
• 20. CMV high risk mismatch (D+/R-)
• 21. History of central nervous system (CNS) infection
• 22. History of active inflammatory bowel disease, chronic diarrhea, or malabsorption
• 23. History of malignancy, per discretion of oncology consult and study oversight team, will be permitted to participate
• 24. History of AL amyloidosis
• 25. Patients who are administered or intended to be administered induction therapy (cytolytic agents such as anti-thymocyte globulin or anti-IL2R therapies such as basiliximab) in the immediate peri- transplant period
• 26. Patients who have undergone desensitization or received therapeutic interventions that are used for the purpose of desensitization prior to transplant
• 27. cPRA calculated by Single Antigen Bead (SAB) testing \> 25% at the time of transplant or any donor specific antibodies before or at the time of transplant (local lab)
• 28. Patients who have been treated with immunosuppressive biologics within 3 months prior to transplant (non-immunosuppressive biologics must have been stopped at the time of transplant)
• 29. Patients for whom there is an intent to administer biologics other than those indicated by protocol during the study period
• 30. Patients who are administered or intended to be administered high dose (\>=2g/kg) intravenous immunoglobulin in the immediate post-transplant period
• 31. A personal history of severe hypogammaglobulinemia (\<300mg/dL)
• 32. Receipt of a live vaccine within 30 days prior to randomization
• 33. Intent to use any other investigational drugs after transplantation
• 34. Past or current medical problems or findings from physical examination or laboratory testing that are not listed above, which, in the opinion of the investigator, may pose additional risks from participation in the study, may interfere with the participant's ability to comply with study requirements, or that may impact the quality or interpretation of the data obtained from the study