A Study of the Drugs Talazoparib and Temozolomide in Prostate Cancer

Inclusion Criteria: * Willing and able to provide written informed consent and HIPAA authorization for the release of personal health information or have their legally authorized representative provide written informed consent. A signed informed consent must be obtained prior to performing screening procedures. NOTE: HIPAA authorization may be either included in the informed consent or obtained separately * Males 18 years of age or above * Histologically or cytologically confirmed adenocarcinoma of the prostate * Bilateral orchiectomy or ongoing androgen deprivation therapy with a GnRH agonist/antagonist (surgical or medical castration) * Progression of mCRPC on treatment with at least 1 second generation hormonal agent (e.g., enzalutamide and/or abirateroneacetate/prednisone) * Documented progressive mCRPC based on at least one of the following criteria: * PSA progression defined as at least 2 rises in PSA with a minimum of a 1-week interval * 1.0 ng/mL is the minimal starting value if confirmed rise is only indication of progression * Soft-tissue progression per RECISTv1.1 * Progression of bone disease (evaluable disease) or tow or more new bone lesions by bone scan * Metastatic disease documented by bone lesions on whole-body radionuclide bone scan or soft tissue disease by computed tomography/magnetic-resonance imaging (CT/MRI). * Consent to a fresh tumor biopsy during screening or have sufficient archival tumor tissue available for molecular profile and biomarker analyses * ECOG status of 0 or 1 (Appendix A: Performance Status Criteria) * Serum testosterone \</= 50mg/dL at screening * Adequate organ function with acceptable initial laboratory values within 14 days of treatment start: Absolute neutrophil count (ANC): \>/= 1,500/ul Hemoglobin: \>/= 9g/dL Platelet count: \>/= 100,00/ul Creatinine: \>/= 60 mL/min estimated using the Cockcroft-Gault equation Potassium: \>/= 3.5 mmol/L (within institutional normal range) Bilirubin: \</= 1.5 ULN (unless documented Gilbert's disease) SGOT(AST): \</= 2.5 x ULN SGPT (ALT): \</= 2.5 x ULN * Patients must agree to use a highly effective method of contraception (e.g., spermicide in conjunction with a barrier such as a condom) or sexual abstinence during treatment, and for at least 7 months after completing therapy. Furthermore, male patients with female partners of reproductive potential and pregnant partners must use a condom (even after vasectomy), during treatment and for at least 4 months after the final dose. Sperm donation is prohibited during the study and for 30 days after the last dose of study drug. Female partners must use hormonal or barrio contraception unless postmenopausal or abstinent. Exclusion Criteria: * Prior treatment with a taxane-based chemotherapy for mCRPC (prior treatment with a taxane-based chemotherapy for metastatic non-castrate prostate cancer is permitted) * Prior treatment with a PARP inhibitor, platinum, cyclophosphamide, mitozantrone chemotherapy, ortemozolmide * Patient has received radiation therapy within 3 weeks (within 2 weeks, if single fraction of radiotherapy) of treatment start * Documented carrier of a pathogenic or likely pathogenic germline or somatic mutation in BRCA 1, BRC 2 or ATM or known carrier (pathogenic or likely pathogenic) or one of the following DNA Damage Repair genes considered as sensitizing tumors to PARP inhibitors: FANCA, CHECK2, PALB2, MRE11A, NBN, RAD51C, ATR, MLH1, and CDK12. Testing is required for BRCA 1, BRCA 1, or ATM. If a patient has had next generation sequencing that did not include FANCA, CHECK2, PALB2, MRE11A, NBN, RAD51C, ATR, MLH1, or CDK12 he will not be excluded from the study if status is unknown. Note, if testing is germline negative, somatic testing is still required. If the patient is germline positive, the patient is ineligible. * Use of systemic hormonal (except for GnRH analog), biologic, radium-223, or any investigational therapy for treatment of metastatic prostate cancer within 4 weeks prior to treatment start. Exceptions include abiraterone, which may not have been administered within 2 weeks of treatment start. * Use of Lutetium (177Lu) vipivotide tetraxetan within 4 weeks prior to treatment start. * Medical conditions such as uncontrolled hypertension, uncontrolled diabetes mellitus, or cardiac disease that would, in the opinion of the investigator, make this protocol unreasonably hazardous to the patient. * Known or suspected brain metastasis or active leptomeningeal disease. * Symptomatic or impending spinal cord compression or cauda equine syndrome * Diagnosis of myelodysplastic syndrome (MDS) * History of another cancer within 2 years of treatment start with the exception of nonmelanoma skin cancers or American Joint Committee on Cancer stage 0 or stage 1 cancer that has a remote probability of recurrence in the opinion of the investigator and the Sponsor * Use of any prohibited concomitant medications (Appendix C: Medications With the Potential for Drug-Drug Interactions) within 14 days prior to the first dose of talazoparib * Grade \> 2 treatment-related toxicity unresolved from prior therapy * Known allergy to any of the compounds under investigation * Any other condition which, in the opinion of the investigator, would preclude participation in this trial