Nivolumab and BMS-986253 for Hormone-Sensitive Prostate Cancer (MAGIC-8)

Inclusion Criteria: * Histologically documented prostatic adenocarcinoma confirmed by a pathology report from prostate biopsy or a radical prostatectomy specimen. * Age ≥18 years * Previously undergone primary therapy for prostate cancer. Salvage XRT or cryotherapy following primary therapy ≥ 6 months prior to randomization is allowed. * A rising PSA defined as the following: * If the subject's primary therapy was RP (radical prostatectomy) (with or without adjuvant or salvage XRT), rising PSA is defined as 2 consecutive rising values above 0.2 ng/mL, each taken ≥ 3 weeks apart, and the last value ≥ 2.0 ng/mL * If the subject received other primary therapies (e.g. XRT, cryosurgery, brachytherapy), rising PSA is defined per the Phoenix definition, i.e., 2 consecutive rising values above the PSA nadir plus 2.0 ng/mL. * For the biopsy sub-groups, patients must be willing to undergo pre and on- treatment biopsies. * PSADT ≤ 12 months. PSADT(prostate-specific antigen doubling time) will be determined from all non-zero PSA values collected preferably, however not limited to, from the 12 months prior to randomization. To calculate PSADT, there must be at least THREE PSA values, with at least 4 weeks between each measurement. The PSADT will be computed from the formula: PSADT = (loge2)/k, with k being the estimated slope of the logarithm of PSA over time. The following web site may also be used: http://www.mskcc.org/applications/nomograms/prostate/PsaDoublingTime.aspx * Eastern Cooperative Oncology Group (ECOG) performance status 0-1, or Karnofsky score ≥ 70% (see Appendix A) * Testosterone ≥ 150 ng/dL ≤ 28 days of prior to registration * Adequate bone marrow, hepatic, and renal function: * White Blood Cell (WBC)\>3,000 cells/mm3 * Absolute neutrophil count (ANC)\>1,500 cells/mm3 * Hemoglobin \>9.0 g/dL * Platelet count \>100,000 cells/mm3 * Serum creatinine \<1.5 × upper limit of normal (ULN) * Serum total bilirubin \<1.5 × ULN * ALT (alanine aminotransferase) \<3 × ULN * AST(aspartate aminotransferase) \<3 × ULN * Willingness to provide written informed consent and HIPAA authorization for the release of personal health information, and the ability to comply with the study requirements (note: HIPAA authorization will be included in the informed consent) * Willingness to use barrier contraception during treatment plus 5 half-lives of nivolumab (\~125 days) plus 90 days (duration of sperm turnover) for a total of 215 days post-treatment completion (azoospermic men are not exempt from contraceptive requirements) Exclusion Criteria: Received any experimental immunotherapy on an experimental clinical trial ≤ 1 year prior to randomization * PSA \> 50 at time of enrollment * High volume disease defined as \>5 bone metastases or lymph nodes \>3cm in size. * Histologic predominance of other types of prostate cancers such as sarcomatous, lymphoma, small cell, and neuroendocrine tumors (note: a maximum of 5 subjects with ductal prostate cancer will be allowed to enroll to each arm of study treatment across all sites). * Received salvage XRT ≤ 6 months prior to randomization * Received ADT ≤ 6 months prior to randomization * Received any form of chemotherapy ≤ 90 days prior to randomization * Received granulocyte colony-stimulating factor or GM-CSF ≤ 90 days prior to randomization * Any major surgery requiring general anesthesia ≤ 28 days prior to randomization. * Any other concurrent or prior treatment for prostate cancer ≤ 28 days prior to randomization. * An active infection requiring parenteral antibiotic therapy or causing fever (temperature \> 100.5 o F or 38.1 o C) within 1 week prior to randomization * Prior systemic, ongoing immunosuppressive therapy ≤ 14 days prior to study treatment administration (except for adrenal replacement steroid doses ≤ 10mgdaily prednisone equivalent in the absence of active autoimmune disease or a short course of steroids (\<5 days) up to 7 days prior to initiating study treatment). * Prior participation in an anti-IL8 clinical study * A candidate is scheduled or likely to be scheduled for salvage external beam XRT or surgery for prostate cancer during the study period * Concomitant treatment with other hormonal therapy or 5α-reductase inhibitors such as Dutasteride or Finasteride (prior use of these agents is allowed if ≥3 months prior to randomization). * History of known or suspected autoimmune disease with the following exceptions: * Asthma and/or allergic rhinitis (seasonal allergies) * Vitiligo * Resolved childhood atopic dermatitis * Psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. * Residual hypothyroidism due to an autoimmune condition only requiring hormone replacement * Euthyroid participants with a history of Grave's disease (participants with suspected autoimmune thyroid disorders must be negative for thyroglobulin and thyroid peroxidase antibodies and thyroid stimulating immunoglobulin (Ig) prior to the first dose of study treatment). * Type 1 diabetes mellitus * History of malignancy within the last 2 years (except non-melanoma skin cancers and superficial bladder cancer) and for which no additional therapy is required or anticipated to be required during the study period. * Uncontrolled major active infectious, cardiovascular, pulmonary, hematologic, or psychiatric illnesses that would make the patient a poor study candidate * Known prior or current history of HIV and/or hepatitis B/C * Prior organ allograft