pTVG-HP and Nivolumab in Patients With Non-Metastatic PSA-Recurrent Prostate Cancer

Inclusion Criteria: * Patients must be at least 18 years of age with a histologic diagnosis of adenocarcinoma of the prostate * Patients must have undergone radical prostatectomy * Patients must have completed local therapy by surgery and any adjuvant/salvage radiation therapy at least 3 months prior to entry, with removal or ablation of all visible disease, including seminal vesical and/or local lymph node involvement. * Patients must have biochemically recurrent, non-metastatic (by CT and bone scan) clinical stage D0/M0 disease defined by the following: * Patients must have evidence of detectable serum PSA with at least 4 serum PSA measurements available, from the same clinical laboratory, at least two weeks apart up to one year, and the final serum PSA value must be \> 2.0 ng/mL. * PSA doubling time, calculated from most recent 4 serum PSA values (collected up to one year prior to enrollment, at least 2 weeks apart, and all from the same clinical laboratory), must be a positive number (i.e. evidence of PSA rise over time). * PSA doubling time will be calculated using the Memorial Sloan-Kettering Cancer Center nomogram (http://www.mskcc.org/applications/nomograms/prostate/PsaDoublingTime.aspx). * Patients must not have definitive evidence of metastases as determined by CT of the abdomen/pelvis and bone scintigraphy (bone scan). Note: patients with lesions detectable by highly sensitive methods (e.g. NaF PET imaging or PSMA PET imaging) will be considered eligible as long as these lesions do not meet size criteria on CT imaging (visceral lesions suspicious for metastases or lymph node \> 15 mm in short axis) and/or are not independently observed on bone scan * Patients with a prior history of a second malignancy are eligible provided they have been treated with curative intent and have been free of disease greater than three years. There will be no exclusion for patients with a history of basal cell carcinoma, squamous cell skin cancer, superficial bladder cancer, or other in situ carcinoma that has been adequately treated. * Patients who are sexually active must use a reliable form of contraception while on study and for 4 weeks after the last immunization. * ECOG performance score \< 2 and life expectancy of at least 12 months. * Patients must have normal hematologic, renal and liver function as defined by: WBC \> 3000/mm3, hematocrit \> 30%, platelet count \> 100,000/mm3, serum creatinine \< 1.5 mg/dl or a calculated creatinine clearance \> 60 cc/min, AST or ALT \< 3.0x ULN, and serum bilirubin \< 2.0 mg/dl(except participants with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL), within 4 weeks prior to first immunization. * Patients must be informed of the experimental nature of the study and its potential risks and must sign an IRB-approved written informed consent form indicating such an understanding. * Willingness to provide blood samples for immune studies, per study calendar, up to one year after study, even if off study treatment. Exclusion Criteria: * Small cell or other variant prostate cancer histology * Patients cannot have evidence of immunosuppression or have been treated with immunosuppressive therapy, such as chemotherapy or chronic treatment dose corticosteroids (greater than the equivalent of 10 mg prednisone per day), within 3 months of the first vaccination. * Seropositive for HIV, hepatitis B (HBV) or hepatitis C (HCV) per patient history due to the immunosuppressive features of these diseases. * Prior treatment with an LHRH agonist or nonsteroidal antiandrogen, except in the following circumstances: Neoadjuvant/adjuvant androgen deprivation therapy administered with radiation therapy or at the time of prostatectomy is acceptable, provided that there was no evidence of PSA progression while on treatment. In this situation, patients must not have received more than 24 months of androgen deprivation treatment. Other treatment with androgen deprivation therapy is prohibited. * Serum testosterone at screening \< 50 ng/dL. * Patients must not be concurrently taking other medications or supplements with known hormonal effects, including PC-SPES, megestrol acetate, finasteride, ketoconazole, estradiol, or Saw Palmetto. All other medications with possible anticancer effects must be discussed with the PI prior to study entry. * Patients previously treated with herbal supplements as described in 5.B.6 or other potential or experimental therapies for prostate cancer must have discontinued these treatments and completed at least a 4 week washout prior to beginning treatment. * Patients must not have evidence of bone metastases or lymph node involvement as determined by bone scan or CT scan of the abdomen and pelvis within 4 weeks of study registration. Note: Advanced imaging modalities (such as NaF-PET/CT, choline PET/CT, fluciclovine, or PSMA PET scans) will NOT be used to determine evidence of metastases for eligibility purposes or for defining disease progression. * Patients must not have been treated with a prior DNA vaccine therapy for prostate cancer. * Patients must not have known psychological or sociological conditions, addictive disorders or family problems, which would preclude compliance with the protocol. * Patients must not have known allergic reactions to GM-CSF. * Patients with unstable or severe intercurrent medical conditions or laboratory abnormalities that would impart, in the judgment of the PI, excess risk associated with study participation or study agent administration. * Patients cannot have concurrent enrollment on other phase I, II, or III investigational therapeutic treatment studies.