PCI-32765 for Special Cases of Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

-INCLUSION CRITERIA: 1. Cohort 1: Treated and untreated patients age 65 or older and need for therapy Cohort 2: Treated (maximum accrual n=16) and untreated (n=27, evaluable) patients at least 18 years old with 17p deletion or p53 expression by immunohistochemistry or p53 mutation by sequencing analysis. 2. Men and women with histologically confirmed disease as defined by the following: * B-lymphocytosis greater than 5000 cells/microL (may be less than 5000 cells/microL if lymphadenopathy is present with histologic confirmation of lymph node involvement by SLL) * Immunophenotypic profile read by an expert pathologist as consistent with CLL. This will include CD5, CD19, and CD20 expression by the CLL cells typically also with CD23 expression, but CD23 negative cases may be included if there is no t11;14 translocation present. 3. Active disease as defined by at least one of the following: * Weight loss greater than or equal to 10% within the previous 6 months * Extreme fatigue * Fevers of greater than 100.5 degrees F for greater than or equal to 2 weeks without evidence of infection * Night sweats for more than one month without evidence of infection * Evidence of progressive marrow failure as manifested by the development of, or worsening of, anemia and/or thrombocytopenia * Massive or progressive splenomegaly * Massive nodes or clusters or progressive lymphadenopathy * Progressive lymphocytosis with an increase of greater than 50% over a 2 month period, or an anticipated doubling time of less than 6 months * Compensated autoimmune hemolysis 4. Eastern Cooperative Oncology Group (ECOG) performance status of less than or equal to 2 5. ANC greater than 500/microL, platelets greater than 30,000/microL 6. Agreement to use contraception during the study and for 90 days after the last dose of study drug if sexually active and able to bear children 7. Willing and able to participate in all required evaluations and procedures in this study protocol including swallowing capsules without difficulty 8. Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (in accordance with national and local subject privacy regulations) EXCLUSION CRITERIA: 1. Previous radiotherapy, radioimmunotherapy, biological therapy, chemotherapy, or treatment with an investigational product fpr CCL treatement in the last 4 weeks (i.e. intravenous immunoglobulin). 2. Transformed CLL 3. Autoimmune hemolytic anemia or thrombocytopenia requiring steroid therapy 4. Impaired hepatic function: Total bilirubin greater than or equal to 1.5 times upper limit of normal unless dute to Gilbert's disease, AST/ ALT greater than or equal to 2.5 times institutional upper limit of normal unless due to infiltration of the liver. 5. Impaired renal funtion: Creatinine greater than or equal to 2.0 mg/dL or GFR less than or equal to 50ml/min 6. Life-threatening illness, medical condition or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of PCI-32765 PO, or put the study outcomes at undue risk 7. Concomitant immunotherapy, chemotherapy, radiotherapy, corticosteroids (at dosages equivalent to prednisone \> 20 mg/day), or experimental therapy 8. Active Hepatitis B infection 9. HIV infection 10. Female patients: Current pregnancy or unwilling to take oral contraceptives or refrain from pregnancy if of childbearing potential or currently breastfeeding. Male patients who are unwilling to follow the contraception requirements described in this protocol. 11. Psychiatric illness/social situations that would limit the patient s ability to tolerate and/or comply with study requirements. 12. Unable to understand the investigational nature of the study or give informed consent. 13. Individuals \< 18 yrs old 14. Known hypersensitivity to any component of PCI-32765 15. Any prior therapy with PCI 32765 or any other BTK inhibitors. 16. Requires anticoagulation with warfarin. 17. Requires treatment with strong CY3A4/5 and/or CYP2D6 inhibitors (unless no alternative is available).