Belinostat Therapy With Zidovudine for Adult T-Cell Leukemia-Lymphoma

Inclusion Criteria: 1. Histologically or cytologically documented adult T-cell leukemia/lymphoma (ATLL) with the following characteristics: * Any stage of disease, * Aggressive types (for definition of ATLL subtypes see Appendix H), * Documented presence of ATLL cells in peripheral blood by either morphology, histology, flow cytometry or gene rearrangement studies. 2. One of the following: * Initiated AZT/IFNα therapy prior or at the time of enrollment. OR; * Received chemotherapy or other antineoplastic drug therapy ≥ 2 weeks prior to enrollment with the exception of dose-reduced vincristine/and or cyclophosphamide, or high dose steroids, administered for cytoreductive purpose. (Note: Continuation of zidovudine and interferon therapy is allowed.). 3. Presence of ATLL based on morphology, histology, flow cytometry, or T-cell clonality in peripheral blood during screening period prior enrollment. 4. Documented Human T-cell lymphotropic virus type 1 (HTLV-1) infection: Documentation may be serologic assay (ELISA) confirmed by Western blot or polymerase chain reaction (PCR). 5. Measurable or evaluable disease, including presence of ATLL by immunophenotyping from either histology or flow cytometry studies, or molecular disease as evidence by T-cell clonality detected by gene rearrangement studies. 6. 18 years of age or older. 7. Karnofsky performance status (KPS) ≥ 50% or Eastern Cooperative Oncology Group (ECOG) performance status ≤ 3 8. Patients must have adequate end organ and bone marrow function as defined below: * absolute neutrophil count (ANC) ≥ 1,000 cells/mm3 \[Exception: Unless cytopenias are secondary to ATLL\] * platelets (PLT) ≥ 50,000 cells/mm3 \[Exception: Unless cytopenias are secondary to ATLL\] * Adequate hepatic function: * transaminase ≤ 2.5 the institutional upper limit of normal (ULN), * total bilirubin ≤ 1.5 x the institutional upper limit of normal (ULN), \[Exception: Unless secondary to hepatic infiltration with lymphoma. If the elevated bilirubin is felt to be secondary to Indinavir or Atazavinir therapy (or anti-HIV medications), patients will be allowed to enroll.\] * Creatinine clearance (CrCl) ≥ 40 mL/min, \[Exception: Unless secondary to renal involvement by lymphoma is suspected.\] 9. Patients who are human immunodeficiency virus positive (HIV+) are also eligible. 10. Females of childbearing potential (CBP) must have a negative serum pregnancy test within one week of enrollment. Women should avoid pregnancy while receiving study treatment. Males and females must agree to use adequate birth control during participation in this trial and for 3 months after completing therapy. 11. Patients receiving erythropoietin or Granulocyte-colony stimulating factor (G-CSF) from baseline are eligible. Exclusion Criteria: 1. Patients with progressive disease (after previous chemotherapy or AZT/IFNα) at the time of enrollment. 2. Patients with chronic leukemia with favorable features, or smoldering type ATLL. 3. Patients receiving any other investigational agents within 14 days prior to initiation of study therapy. (Exception: Patients actively receiving IFN-alfa-2b, PEG-IFN-alfa-2b, or similar forms of IFN-alfa are permitted). 4. Uncontrolled inter-current illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (CHF), unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that are likely in the judgment of the Investigator(s) to interfere or limit compliance with study requirements/treatment. 5. Pregnant or breast-feeding women. 6. Known hypersensitivity to histone deacetylases (HDACs), zidovudine, belinostat or any component of the formulation(s). 7. Acute hepatitis or decompensated liver disease unless due to lymphoma. Chronic hepatitis will be required to be on prophylactic treatment during the study if provided liver function test meet criteria listed above without evidence of cirrhosis to be eligible. 8. Concurrent active malignancies, with the exception of in situ carcinoma of the cervix, non-metastatic, non-melanomatous skin cancer, or Kaposi's sarcoma not requiring systemic chemotherapy. 9. Known New York Heart Association (NYHA) Class 3 or 4 heart disease as per Appendix D. 10. Known ejection fraction \< 45% or institutional limit of normal range 11. Psychological, familial, sociological or geographical conditions likely in the judgment of the Investigator(s) to interfere or limit compliance with study requirements/treatment.