Inclusion Criteria:

1. FOR TREATMENT-NAIVE GROUP ONLY: Men and women ≥ 65 years of age with confirmed diagnosis of CLL/SLL, who require treatment per NCI or International Working Group guidelines11-14
2. FOR RELAPSED/REFRACTORY GROUP ONLY: Men and women ≥ 18 years of age with a confirmed diagnosis of relapsed/refractory CLL/SLL unresponsive to therapy (ie, failed ≥ 2 previous treatments for CLL/SLL and at least 1 regimen had to have had a purine analog [eg, fludarabine] for subjects with CLL)
3. Body weight ≥ 40 kg
4. ECOG performance status of ≤ 2
5. Agreement to use contraception during the study and for 30 days after the last dose of study drug if sexually active and able to bear children
6. Willing and able to participate in all required evaluations and procedures in this study protocol including swallowing capsules without difficulty
7. 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. A 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
2. Any immunotherapy, chemotherapy, radiotherapy, or experimental therapy within 4 weeks before first dose of study drug (corticosteroids for disease-related symptoms allowed but require 1-week washout before study drug administration)
3. Central nervous system (CNS) involvement by lymphoma
4. Major surgery within 4 weeks before first dose of study drug
5. Creatinine > 1.5 x institutional upper limit of normal (ULN); total bilirubin > 1.5 x ULN (unless due to Gilbert's disease); and aspartate aminotransferase (AST) or alanine aminotransferase (ALT) > 2.5 x ULN unless disease related
6. Concomitant use of medicines known to cause QT prolongation or torsades de pointes
7. Significant screening electrocardiogram (ECG) abnormalities including left bundle branch block, 2nd degree AV block type II, 3rd degree block, bradycardia, and QTc > 470 msec
8. Lactating or pregnant