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 may have received prior radiation, chemoembolization, radioembolization or
             other local ablative therapies or hepatic resection if completed ≥ 4 weeks prior to
             registration AND if patient has recovered to <= grade 1 toxicity. Extrahepatic
             palliative radiation is permitted if completed ≥ 2 weeks prior to enrollment AND if
             patient has recovered to ≤ grade 1 toxicity.

          -  Patients must have radiographically measurable disease 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.

          -  Must be ≥18 years of age

          -  Must have a Child-Pugh score of A (prognosis in chronic liver disease and cirrhosis)

          -  Must have an ECOG (Eastern Cooperative Oncology Group) performance status of 0-1

          -  Ability to understand and willingness to sign IRB-approved informed consent

          -  Willing to provide archived tissue, if available, from a previous diagnostic biopsy

          -  Must be able to tolerate CT (computerized tomography) and/or MRI (magnetic resonance
             imaging) with contrast

          -  Must have adequate organ function obtained ≤ 2 weeks prior to registration

        Exclusion Criteria:

          -  Patients may not have received prior systemic treatment (chemotherapy or targeted
             therapy) for advanced BTC (biliary tract cancer). Prior adjuvant chemotherapy is
             permitted provided it was completed > 6 months from registration.

          -  Must not have a diagnosis of immunodeficiency, or have received systemic steroid
             therapy, or any other form of immunosuppressive therapy within 7 days prior to trial
             treatment.

          -  Must not have known Hepatitis B, Hepatitis C, or HIV seropositivity. Testing is not
             required in absence of clinical suspicion.

          -  Must not have prior history of organ transplantation or brain metastasis.

          -  Must not have undergone a major surgical procedure < 4 weeks prior to registration.

          -  Must not have an 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.

          -  Must have no ongoing active, uncontrolled infections

          -  Must not have received a live vaccine within 30 days of planned start of the study
             therapy.

          -  Must not 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.

          -  Women must not be pregnant or breastfeeding since study drugs may harm the fetus or
             child.

          -  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 5 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 are excluded. 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 7
             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.