-  INCLUSION CRITERIA:

               1. Patients with histologically or cytologically confirmed cholangiocarcinoma by the
                  NCI Laboratory of Pathology. Archival tumor sample may be used but if archival
                  tissue is not available or is not adequate, tissue biopsy will be required.

               2. Patients must have cholangiocarcinoma that is not amenable to resection.

               3. Patients must have had prior treatment with 1st line chemotherapy.

               4. Disease must be measurable by Response Evaluation Criteria in Solid Tumors
                  (RECIST) criteria Version 1.1.

               5. Age >=18 years.

                  NOTE: Because no dosing or adverse event data are currently available on the use
                  of tivozanib in subjects < 18 years of age, children are excluded from this
                  study, but may be eligible for future pediatric trials.

               6. ECOG performance status <= 1

               7. If the patient has liver disease; Child Pugh Class A.

               8. Adequate organ and marrow function as defined below:

                    -  Hemoglobin >= 9.0 g/dL

                    -  Absolute neutrophil count >= 1,000/mcL

                    -  Platelets >= 75,000/mcL

                    -  Total bilirubin <= 2 X institutional upper limit of normal (ULN)

                    -  AST(SGOT)/ALT(SGPT) <= 5 X institutional ULN

                    -  Creatinine clearance >= 60 mL/min/1.73 m^2 calculated by calculated using
                       eGRF in the clinical lab

                    -  Serum Albumin (g/L) > 35

                    -  Alkaline phosphatase** <= 2.5 x ULN

                       **unless bony metastases present

                    -  INR < 1.7

               9. Negative serum or urine pregnancy test at screening for women of childbearing
                  potential (WOCBP).

                  NOTE: WOCBP is defined as any female who has experienced menarche and who has not
                  undergone successful surgical sterilization or who is not postmenopausal. WOCBP
                  must have a negative pregnancy test (HCG blood or urine) during screening.

              10. Women of child-bearing potential and men must agree to use adequate contraception
                  (hormonal or barrier method of birth control; abstinence) prior to study entry,
                  for the duration of study participation, and 1 month after completion of
                  treatment.

              11. Ability of subject to understand and the willingness to sign a written informed
                  consent document.

              12. Ability and willingness to co-enroll on the tissue collection protocol 13C0176,
                  "Tumor, Normal Tissue and Specimens from Patients Undergoing Evaluation or
                  Surgical Resection of Solid Tumors".

        EXCLUSION CRITERIA:

          1. Chemotherapy, small molecule or radiation therapy within 3 weeks prior to
             administration of first dose of study drug.

          2. Prior treatment with Tivozanib.

          3. Any history of elevations of both total serum bilirubin > 2X ULN AND AST or ALT > 3X
             ULN, unless related to common bile duct obstruction and treated adequately with a
             stent.

          4. History of hepatic encephalopathy within past 12 months or requirement for medications
             to prevent or control encephalopathy (e.g., no lactulose, rifaximin, etc. if used for
             purposes of hepatic encephalopathy).

          5. Inadequate recovery from any prior surgical procedure or major surgical procedure
             within 4 weeks prior to administration of first dose of study drug.

          6. Patients with previous malignant disease other than the target malignancy within the
             last 3 years with the exception of basal or squamous cell carcinoma of the skin,
             cervical carcinoma in situ or thyroid carcinoma.

          7. Current active second primary malignancy, other than skin carcinoma (basal or squamous
             cell carcinoma) or differentiated thyroid carcinoma.

          8. History of allergic reactions or known or suspected hypersensitivity attributed to
             compounds of similar chemical or biologic composition to tivozanib.

          9. Patients with uncontrolled intercurrent illness including, but not limited to, ongoing
             or active infection requiring systemic therapy (see exceptions below), or psychiatric
             illness/social situations that would limit compliance with study requirements

               -  Human immunodeficiency virus (HIV)-infected patients on effective anti-
                  retroviral therapy with undetectable viral load within 6 months are eligible for
                  this trial.

               -  For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV
                  viral load must be undetectable and on suppressive therapy, if indicated.

               -  Patients with a history of hepatitis C virus (HCV) infection must have been
                  treated and cured. For patients with HCV infection who are currently on
                  treatment, they are eligible if they have an undetectable HCV viral load.

         10. Significant cardiovascular disease, including: Active clinically symptomatic left
             ventricular failure, uncontrolled hypertension, myocardial infarction, severe angina,
             or unstable angina within 6 months prior to administration of first dose of study
             drug, history of serious ventricular arrhythmia, cardiac arrhythmias requiring
             anti-arrhythmic medications.

         11. Uncontrolled hypertension, i.e., blood pressure (BP) of >= 180/95; patients 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.

         12. Significant hematologic, gastrointestinal, thromboembolic, vascular, bleeding, or
             coagulation disorders.

         13. GI Bleeding (e.g., esophageal varices or ulcer bleeding) within 12 months. (Note: For
             patients with a history of GI bleeding for more than 12 months or assessed as high
             risk for esophageal variceal by the Investigator, adequate endoscopic therapy
             according to institutional standards is required.)

         14. Clinically meaningful ascites defined as ascites requiring non-pharmacologic
             intervention (e.g., paracentesis) to maintain symptomatic control, within 6 months
             prior to the first scheduled dose. Subjects on stable doses of diuretics for ascites
             for >= 2 months are eligible.

         15. Main portal vein thrombosis (Vp4) as documented on imaging. (VP4 is defined as portal
             vein thrombosis in the main trunk of the portal vein or a portal vein branch
             contralateral to the primarily involved lobe (or both).)

         16. Complex biliary obstruction requiring bile duct stents at more than one level of the
             biliary tree or external biliary drainage.

         17. Recurrent episodes of cholangitis (>1) in the preceding 3 months prior to enrollment.

         18. Therapeutic anti-coagulation or anti-platelet therapy with the exception of low
             molecular weight heparin or aspirin.

         19. Pregnant or lactating women. Pregnant women are excluded from this study because based
             on findings in animals and its mechanism of action, tivozanib can cause fetal harm
             when administered to a pregnant woman. In animal reproduction studies, administration
             of tivozanib to pregnant rats caused adverse developmental outcomes including embryo-
             fetal mortality. Because there is an unknown but potential risk for adverse events in
             nursing infants secondary to treatment of the mother with tivozanib, breastfeeding
             should be discontinued if the mother is treated with tivozanib. These potential risks
             may also apply to other agents used in this study.

         20. Treatment with systemic hormonal therapy within 3 weeks prior to start of protocol
             therapy, with the exception of:

               -  Hormonal therapy for appetite stimulation or contraception

               -  Nasal, ophthalmic, inhaled and topical steroid preparations

               -  Oral replacement therapy for adrenal insufficiency

               -  Low-dose maintenance steroid therapy (equivalent of prednisone 10 mg/day) for
                  other conditions

               -  Hormone replacement therapy