Belatacept in Heart Transplantation

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 (VCA IgG, EBNA IgG). If EBNA is not available, enrollment may proceed but the result must be available prior to randomization. 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 (niaidtransplantstudies.org) 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. Pre-transplant eGFR (CKD-epi) \>30ml/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 active Tuberculosis (TB) in the past 2 years, whether or not it was adequately treated; patients with documented treatment of active TB greater than 2 years ago will be allowed to participate if there is documentation of adequate treatment according to locally accepted clinical practice 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. Participants currently or formerly residing in regions of the US that are highly endemic for coccidiomycosis will undergo serological testing, as per the site's standard of care. Participants with positive serology who have previously been fully treated, will be permitted to participate pending full treatment, and then require prophylaxis as further outlined in Section 7 for the duration of the study. Participants with negative serology who reside in regions where coccidiomycosis is endemic are eligible for enrollment only if they receive prophylaxis for the duration of the study. Endemic regions are determined by site based on local standard of care 16. Findings on pre-transplant or pre-randomization chest x-ray or CT scan suggestive of fungal infection where an alternative etiology is not identified. Participants with a history of positive serologies for histoplasmosis or blastomycosis, performed for clinical indications will be permitted to participate if they have a normal chest x-ray or CT scan but require prophylaxis 17. 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 18. Current white blood cell (WBC) count \<3.0 or an absolute neutrophil count (ANC) of less than 1500 cells/mm\^3 or recurrent leukopenia that is likely to necessitate immunosuppression reduction after transplant, as determined by the site PI 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 p