Rucaparib in Combination With Nivolumab in Patients With Advanced or Metastatic Biliary Tract Cancer Following Platinum Therapy

Inclusion Criteria * Patients must have a pathologically confirmed adenocarcinoma of the biliary tract (intra-hepatic, extra-hepatic (hilar, distal) or gall bladder) that is not eligible for curative resection, transplantation, or ablative therapies. Tumors of mixed histology are excluded. * Patients must have received 1st line platinum-based systemic chemotherapy for advanced BTC for 4-6 months without radiologic or clinical progression. Last systemic infusion of 1st line platinum-based therapy may not be more than 4 weeks from study informed consent. Prior peri-operative chemotherapy is permitted provided it was completed \> 6 months from start of platinum-based therapy for advanced disease. * Prior surgical resection, radiation, chemoembolization, radioembolization or other local ablative therapies are permitted if completed \> 4 weeks prior to enrollment AND if patient has recovered to \< 1 grade 1 toxicity. * Patients must have measurable disease (as per RECISTv1.1) in at least one site not previously treated with radiation or liver directed therapy (including bland, chemo- or radio-embolization, or ablation) either within the liver or in a metastatic site unless the patient has had complete response to 1st line platinum-based therapy. * Age≥18 years * Child-Pugh score of A or B7 (Scoring system used to assess the prognosis of chronic liver disease, mainly cirrhosis) * ECOG performance status of 0-1 (Eastern Cooperative Oncology Group scoring system used to quantify general well-being and activities of daily life; scores range from 0 to 5 where 0 represents perfect health and 5 represents death.) * Ability to understand and willingness to sign IRB-approved informed consent * Available archived tissue (FFPE block or 20 unstained slides from prior core biopsy or surgery) * Must be able to tolerate CT and/or MRI with contrast * Adequate organ function obtained ≤ 2 weeks prior to registration Exclusion Criteria * Diagnosis of immunodeficiency, or received systemic steroid therapy, or any other form of immunosuppressive therapy within 14 days prior to trial treatment. Short bursts of steroids of 5-7 days (for COPD exacerbation or other similar indication) are allowed. * Prior history of solid organ transplantation or brain metastasis (unless treated and stable) * Patients may not have undergone a major surgical procedure \< 4 weeks prior to registration * Active second malignancy other than non-melanoma skin cancer or cervical carcinoma in situ. Patients with history of malignancy are eligible provided primary treatment of that cancer was completed \> 1 year prior to registration and the patient is free of clinical or radiologic evidence of recurrent or progressive malignancy. * Ongoing active, uncontrolled infections (afebrile for \> 48 hours off antibiotics) * Have received a live vaccine within 30 days of planned start of the study therapy * Have a psychiatric illness, other significant medical illness, or social situation which, in the investigator's opinion, would limit compliance or ability to comply with study requirements * Pregnant or breastfeeding since rucaparib and/or nivolumab may harm the fetus or child. All females of childbearing potential (not surgically sterilized and between menarche and 1-year post menopause) must have a blood or urine test to rule out pregnancy within 2 weeks prior to registration. * Women of child-bearing potential and men must agree to use 2 methods of adequate contraception (hormonal plus barrier or 2 barrier forms) OR abstinence prior to study entry, for the duration of study participation, and for 6 months (for women) and 7 months (for men) following completion of study therapy * Participants with an active, known or suspected autoimmune disease which may affect vital organ function, or has/may require systemic immunosuppressive therapy for management. Participants with type I diabetes mellitus, hypothyroidism only requiring hormone replacement, skin disorders (such as vitiligo, psoriasis, or alopecia) not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. * Participants with a condition requiring systemic treatment with either corticosteroids (\>10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of start of study treatment. Inhaled or topical steroids, and adrenal replacement steroid doses \>10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease. * Patients may not have previously received anti PD1/PDL1 antibodies or PARP inhibitor for treatment of this cancer.