The Purpose of This Research Study is to See if Combining Gemcitabine, Cisplatin and Durvalumab Chemotherapy Treatments With a Direct Tumor Therapy Yittrium-90 (Y-90) Will Work Better Together to Shrink Tumors and Control Cancer

Inclusion Criteria:

* Adult males and females at least 18 years of age
* Histologically and/or cytologically confirmed iCCA that is previously untreated or, if systemic therapy has been rendered for prior disease, has been administered at least 6 months before the development of recurrent or de novo new sites of disease.
* Unresectable disease, as deemed by the Inova multidisciplinary tumor board (i.e. disease that cannot be safely resected with negative margins, leaving 2 adjacent segments of liver with intact portal venous and hepatic arterial inflow and intact biliary and hepatic venous outflow with the future liver remnant of sufficient volume to avoid postoperative liver insufficiency)
* Measurable disease per RECIST 1.1 at least 2 cm in size
* Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1
* Noncirrhotic liver - patients should not have a preexisting diagnosis of cirrhosis either diagnosed via biopsy or with features consistent with cirrhosis on imaging (e.g. shrunken liver with nodularity consistent with cirrhosis). Child-Pugh score must be less than 5.
* No evidence of extrahepatic disease, except for regional adenopathy that would be resected as part of a standard oncologic surgical procedure
* Adequate organ function as indicated by the following laboratory values (Table 1)
* Ability to complete testing in the protocol
* Able and willing to consent to protocol

Exclusion Criteria:

* Female patients who are pregnant or breast-feeding
* History of allogeneic organ transplantation.
* Active or history of autoimmune disease or immune deficiency, including, but not limited to, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjögren syndrome, Guillain-Barré syndrome, or multiple sclerosis, with the following exceptions:

  * Patients with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone are eligible for the study.
  * Patients with controlled type 1 diabetes on an insulin regimen are eligible for the study.
  * Patients with vitiligo or alopecia.
  * Any chronic skin condition that does not require systemic therapy.
  * Patients without an active autoimmune disease in the last 5 years may be included but only after consultation with the study physician.
  * Patients with diet controlled celiac disease.
* Current or recent use of immunosuppressive medication within 14 days before durvalumab initiation except if:

  * Intranasal, inhaled, topical or local steroid injections
  * Systemic corticosteroids at physiologic doses that do not exceed 10 mg/day of prednisone or its equivalent.
  * Steroids as premedication for hypersensitivity reactions, (i.e. CT scan premedication).
* Child-Pugh B7 or greater cirrhosis
* Extrahepatic or perihilar cholangiocarcinoma
* Gallbladder cancer
* Pancreatic or ampullary cancer
* Portal vein thrombosis involving the main portal vein or first order right or left portal vein branches
* Extrahepatic disease, other than regional lymph nodes that would be removed at time of surgery as part of a routine oncologic procedure for iCCA
* Previous treatment with chemotherapy, intra-arterial or radiotherapy for iCCA is exclusionary, with the exception of adjuvant therapy with capecitabine which is allowed.
* Contraindication to durvalumab, gemcitabine, or cisplatin
* Active hepatitis B or C for which patients refuse treatment. Patients who are newly diagnosed with active disease as part of protocol screening and are agreeable to initiate on antiviral treatment are allowed to enroll.
* Contraindication found during work-up angiography, including significant lung shunting (lung dose \>30 Gy for a single treatment or \>50 Gy cumulative), or non-manageable extrahepatic deposition of technetium Tc 99m macroaggregated albumin on scintigraphy performed after planning angiography
* \> 75% hepatic tumor burden
* Inability to protect non-target arteries to intestines or solid organs from radioembolization
* Serum albumin \< 3 g/dL
* Serum bilirubin \> 2 mg/dL, serum aspartate aminotransferase or alanine aminotransferase \> 5 times upper limit of normal
* Concomitant illness that would prevent adequate patient assessment or in the investigators' opinion pose an added risk for study participants.
* Life-threatening intercurrent illness
* Anticipated poor compliance
* Prisoners or subjects who are involuntarily incarcerated
* Persons with decisional incapacity/cognitive impairment
* Any history or evidence of severe illness or any other condition that would make the patient, in the opinion of the investigator unsuitable for the study
* Subject is enrolled in a separate interventional clinical trial