Olaparib in Men With High-Risk Biochemically-Recurrent Prostate Cancer Following Radical Prostatectomy, With Integrated Biomarker Analysis

Inclusion Criteria: 1. Histologic diagnosis of adenocarcinoma of the prostate 2. Prior local therapy with prostatectomy required, with available tissue from prostatectomy specimen to send for genomic and transcriptomic testing. 3. Prior salvage or adjuvant radiation therapy is allowed but not mandated. Radiation therapy must have been completed for at least 6 months. 4. Absolute PSA ≥1 ng/ml. Prior undetectable PSA post-prostatectomy is not required. 5. PSADT ≤6 months, based upon ≥3 consecutive measurements collected in the past 12 months, at least 4 weeks apart 6. No radiographic evidence of metastatic disease by CT scan and bone scan, performed within the prior 4 weeks. 7. Serum testosterone ≥ 150 ng/dl 8. Participants must have normal organ and bone marrow function measured within 28 days prior to administration of study treatment as defined below: * Hemoglobin ≥ 10.0 g/dL with no blood transfusion in the past 28 days * Absolute neutrophil count (ANC) ≥ 1.5 x 109/L * Platelet count ≥ 75 x 109/L * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST) (Serum Glutamic Oxaloacetic Transaminase (SGOT)) / Alanine aminotransferase (ALT) (Serum Glutamic Pyruvate Transaminase (SGPT)) \<2.5 x institutional upper limit of normal. Note: Patients with elevations in bilirubin, AST, or ALT should be thoroughly evaluated for the etiology of this abnormality prior to entry and patients with evidence of viral infection should be excluded. * Patients must have creatinine clearance estimated using the Cockcroft * Gault equation of ≥51 mL/min: Estimated creatinine clearance = (140-age \[years\]) x weight (kg) serum creatinine (mg/dL) x 72 9. Eastern Cooperative Oncology Group (ECOG) performance status 0-1 10. Male participants and their partners, who are sexually active and of childbearing potential, must agree to the use of two highly effective forms of contraception in combination \[see appendix F for acceptable methods\], throughout the period of taking study treatment and for 3 months after last dose of study drug to prevent pregnancy in a partner. 11. For enrichment stage of trial only (if necessary): Confirmation of a suspected/known deleterious mutation in a gene of interest (ATM, BARD1, BRCA1, BRCA2, BRIP1, CDK12, CHEK1, CHEK2, FANCL, PALB2, PPP2R2A, RAD51B, RAD51C, RAD51D, or other DNA repair genes) via CLIA certified testing. Exclusion Criteria: 1. Prior ADT in the past 6 months. Prior ADT in context of neoadjuvant/adjuvant primary; prior ADT for biochemical recurrence is allowed, as long as no ADT has been administered in past 6 months and testosterone has recovered (\>150 ng/dl). The total duration of prior ADT should not exceed 24 months. 2. Prior oral anti-androgen (e.g. bicalutamide, nilutamide, enzalutamide, apalutamide), or androgen synthesis inhibitor (e.g. abiraterone, orteronel) in the past 6 months. 5-alpha reductase inhibitor therapy (e.g. finasteride, dutasteride) is allowed, as long as subject has been stable on medication for past 6 months. 3. Prior treatment with intravenous chemotherapy. 4. Involvement in the planning and/or conduct of the study 5. Participation in another clinical study with an investigational product during the last 1 month. 6. Any previous treatment with PARP inhibitor, including olaparib 7. Resting ECG with QTc \> 470 msec on 2 or more time points within a 24 hour period or family history of long QT syndrome 8. Concomitant use of known strong CYP3A inhibitors (eg. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (eg. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting olaparib is 2 weeks. 9. Concomitant use of known strong CYP3A inducers (eg. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort ) or moderate CYP3A inducers (eg. bosentan, efavirenz, modafinil). The required washout period prior to starting olaparib is 5 weeks for phenobarbital and 3 weeks for other agents. 10. Myelodysplastic syndrome/acute myeloid leukaemia or with features suggestive of MDS/AML. 11. Major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery. 12. Poor medical risk due to a serious, uncontrolled medical disorder, non- malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, extensive interstitial bilateral lung disease on High Resolution Computed Tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent. 13. Unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. 14. Immunocompromised patients, e.g., patients who are known to be serologically positive for human immunodeficiency virus (HIV). 15. Known hypersensitivity to olaparib or any of the excipients of the product. 16. Known active hepatitis (i.e. Hepatitis B or C) due to risk of transmitting the infection through blood or other body fluids 17. Whole blood transfusions in the last 120 days prior to entry to the study (packed red blood cells and platelet transfusions are acceptable, for timing refer to inclusion criteria no.10)