Cisplatin Plus Romidepsin & Nivolumab in Locally Recurrent or Metastatic Triple Negative Breast Cancer (TNBC)

Inclusion Criteria: * Subjects must meet at least one of the following two criteria: 1. Histologically proven TNBC 2. Confirmed germline BRCA1 or BRCA2 mutation, regardless of subtype of breast cancer * Breast cancer that is either stage III disease not amenable to curative therapy or stage IV * Have at least one measurable lesion of ≥ 2 cm by conventional methods or ≥ 1 cm on spiral CT * No limit to prior therapy for metastatic breast cancer. Prior treatment with cisplatin is excluded, unless prior cisplatin treatment was given in the neo/adjuvant setting. All other platinum compounds are allowed as long as it has been 6 months since last platinum exposure. * All patients should have received at least one line of chemotherapy in either the advanced or adjuvant setting and hormonal therapy (where appropriate). Participants who have previously been treated with endocrine therapy only, and later develop triple negative disease are eligible as long as they have had one line of chemotherapy in either the advanced or adjuvant setting. * Eastern Oncology Cooperative Group (ECOG) Performance status of ≥ 2 * Laboratory values as follows: * absolute neutrophil count ≥ 1,500/uL (microliter) * platelets ≥ 100,000/uL (no transfusion allowed within 2 weeks) * hemoglobin \> 9 g/dL (which may be reached by transfusion) * total bilirubin within normal range or ≤ 1.5 x IULN (Institutional Upper Limit of Normal) if liver metastases * total bilirubin ≤ 3.0 x IULN with direct bilirubin within normal range in subjects with Gilbert's Syndrome * aspartate aminotransferase (AST) (SGOT) /Alanine transaminase (ALT) (SPGT) ≤ 2.5 x IULN or ≤ 5 x IULN if liver metastases * Serum creatinine ≤ 1.5 x IULN * International Normalized Ratio (INR) ≤ 1.5 * Serum potassium \> 3.8 mmol/L * Serum magnesium \>1.8 mg/dL * IV bisphosphonate and denosumab for bony metastatic disease is allowed * Radiation to bony metastases is allowed ≥ 14 days before starting study treatment * Subjects with previously treated brain metastasis who are free of central nervous system (CNS) symptoms and are ≥ 14 days from treatment of brain metastasis are eligible. * Women of child bearing potential and their partners must use contraception prior to study entry, continuing for 5 months after treatment. Exclusion Criteria: * Subject has received any anti-cancer therapy including chemotherapy, immunotherapy, biologic, targeted therapy, or any investigational therapy within either 14 days or 5 half-lives (whichever is shorter), prior to study drug administration. * Subjects who have not recovered to within one grade level (not to exceed Grade 2) of their baseline following a significant adverse event or toxicity attributed to prior treatment. * Other medical or psychiatric disorder placing the subject at undue risk for treatment complications * Subject is pregnant or lactating * Subject has previously been treated with a Histone deacetylases (HDAC) inhibitor, PD-1 inhibitor, PD-L1 inhibitor, PD-L2 inhibitor, CTLA-4 inhibitor, or any other antibody or drug specifically targeting T-cell costimulation or immune checkpoint pathways * Subject tests positive for hepatitis B or C indicating acute or chronic infection * Subject has known history of testing positive for HIV or AIDS * Subject has inflammatory breast cancer * Subject has a known hypersensitivity to any of the excipients of nivolumab, cisplatin or romidepsin * Subject has a concurrent malignancy or malignancy within 3 years of study enrollment (with the exception of adequately treated, basal or squamous cell carcinoma, non-melanomatous skin cancer or curatively resected cervical cancer or prior ovarian/breast cancer in patients with BRCA associated breast cancer). * Subject is classified into Child-Pugh Class C * Subject has active, uncontrolled infection * Subject has symptomatic/untreated CNS disease * Subject has an active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger. * Subject has active cardiac disease or a history of cardiac dysfunction, including: * Congenital long QT syndrome * Corrected QT interval (QTc) interval ≥ 500 ms on the screening ECG (using the corrected QT interval to Fridericia's formula \[QTcF\]) * Myocardial infarction within 6 months of Cycle 1 Day 1 (C1D1). * Other significant ECG abnormalities including 2nd degree atrio-ventricular (AV) block type II, 3rd degree AV block, or bradycardia (ventricular rate less than 50 beats/min) * Symptomatic coronary artery disease (CAD) * An ECG recorded at screening showing evidence of cardiac ischemia (ST depression of ≥ 2 mm, measured from isoelectric line to the ST segment). * Congestive heart failure (CHF) that meets New York Heart Association (NYHA) Class II to IV definitions and/or ejection fraction \< 40% by Multi Gated Acquisition Scan (MUGA) or \< 50% by echocardiogram and/or MRI * A known history of sustained ventricular tachycardia (VT), ventricular fibrillation (VF), Torsade de Pointes, or cardiac arrest unless currently addressed with an automatic implantable cardioverter defibrillator (AICD) * Hypertrophic cardiomegaly or restrictive cardiomyopathy from prior treatment or other causes * Uncontrolled hypertension, i.e., blood pressure (BP) of ≥ 160/95; subjects who have a history of hypertension controlled by medication must be on a stable dose (for at least one month) and meet all other inclusion criteria * Any cardiac arrhythmia requiring an anti-arrhythmic medication (excluding stable doses of beta-blockers) * Subjects taking drugs leading to significant QT prolongation * Concomitant use of CYP3A4 inhibitors * Subject has had major surgery within 14 days prior to starting study drug or has not recovered from major side effects * Subject is currently receiving or has received systemic corticosteroids ≤ 2 weeks prior to starting study drug or who have not fully recovered from side effects of such treatment. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease. * Subject is currently receiving treatment with drugs known to be moderate or strong inhibitors or inducers of isoenzyme CYP3A. The subject must have discontinued strong inducers for at least one week and must have discontinued strong inhibitors before the start of treatment. * Subject is currently receiving warfarin or other coumarin derived anti-coagulant for treatment. Therapy with heparin, low molecular weight heparin (LMWH), Factor Xa or fondaparinux is allowed. * Subjects with baseline peripheral neuropathy that exceeds Grade 1.