Combination of Entinostat and Enzalutamide in Advanced Prostate Cancer

Inclusion Criteria: Each patient must meet all of the following inclusion criteria to be enrolled in the study: * Age \>/= 18 years and are capable of giving informed consent. Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Patients must have a pathologically confirmed diagnosis of prostate adenocarcinoma. Features of neuroendocrine phenotype are allowed. * Patients must have evidence of castration resistant metastatic disease and eligible for Enzalutamide per standard guidelines. Castration resistant non-metastatic disease is allowed in phase I study if subject is candidate for Enzalutamide. * Patients must have and ECOG performance status of ≤ 2.(appendix D) * Patients must be on continuous LHRH agonist or antagonist treatment or surgically castrated with castrate levels of testosterone (\< 20 ng/dl). * Any number of prior chemotherapy regimens are allowed. Chemotherapy naïve patients are allowed. * If patient is already on Enzalutamide at a dose of 160mg daily, he is allowed if he can have baseline image and PSA within 1 month of the start of entinostat. * Patients may have had androgen synthesis inhibitors or other investigational drugs. Patient must have discontinued flutamide or nilutamide or other AR targeted agents (including abiraterone) for at least 4 weeks and bicalutamide for at least 6 weeks prior to day 1 of treatment. * Patients receiving treatment with bisphosphonates or denosumab must remain on treatment during the study. * Patients must not require concurrent radiation or other chemotherapy while receiving protocol therapy. Patients may have received previous radiation but must have completed radiation at least 4 weeks (8 weeks for radiation to the brain) prior to registration. * Patients must have recovered to grade ≤ 1 from all acute toxicity of previous radiation, hormonal or chemotherapy treatments. * Patient agrees to use an acceptable method for contraception during the entire study treatment period through 4 months after the last dose of entinostat. * Adequate renal function as defined by serum creatinine ≤ 1.5 x ULN. If creatinine \>1.5 x ULN, calculated or measured creatinine clearance must be ≥ 60 mL/minute (Cockcroft-Gault). * ANC \> 1500/mm³, platelets \> 100,000/mm³, Hgb \> 9 g/dL. * Total bilirubin ≤ ULN, SGOT (AST) and SGPT (ALT)\< 1.5 x ULN. AST and/or ALT may be up to 5X ULN in the setting of known liver metastasis. Exclusion Criteria: Patients meeting any of the following exclusion criteria are not to be enrolled in the study: * Patient was treated and discontinued Enzalutamide previously for any reason. * Major surgery within 28 days or serious infection requiring IV antibiotics within 14 days preceding the first dose of study treatment * Patient has received other investigational drugs within 14 days before enrollment. * Known GI disease or GI procedure that could impact drug absorption in the upper bowel, or tolerance of Entinostat. Examples include but are not limited to partial gastrectomy, small bowel resection, pancreatectomy, malabsorption or celiac disease * Ongoing nausea or vomiting of any severity without improvement after appropriate treatment. * \> Grade 1 diarrhea, not controlled with appropriate treatment. * History of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness, such as severe chronic obstructive pulmonary disease requiring supplemental oxygen. * Clinical and/or radiographic evidence of cerebral metastases. However, patients who have a history of central nervous system (CNS) metastasis but who have no radiographic or clinical evidence of residual tumor (eg, following complete surgical resection or stereotactic radiosurgery) are not excluded from participation in this study. * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any EKG abnormality at Screening has to be documented by the investigator as not medically relevant. * Serious medical or psychiatric illness or laboratory abnormality that may increase the risk associated with study participation or investigational product administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for enrollment in this study. * Any other currently active malignancy (excluding controlled non-melanoma skin cancer). Patients are considered NOT to have "currently active" malignancy if they have completed any necessary therapy and are considered by their physician to be at less than 30% risk of relapse. * Treatment with clinically significant enzyme inducers, such as the enzyme-inducing antiepileptic drugs phenytoin, carbamazepine or phenobarbital, or rifampin, rifabutin, rifapentine or St. John's Wort within 14 days prior to the first dose of Entinostat and during the study. * History of seizure and on active therapy for seizure * Known history of uncontrolled human immunodeficiency virus (HIV) infection. HIV positive patients will be allowed if they are on treatment and have an adequate CD4 count (CD4 count \>200). Screening is not required in the absence of clinical findings or suspicion.