Inclusion Criteria:

• Relapsed or refractory CLL and require treatment (Phase 1).
• Relapsed CLL requiring treatment and has received no more than 5 prior treatment regimens (Phase 2a)
• Eastern Cooperative Oncology Group performance score <= 1
• Must be on a stable dose of Selective Serotonin Reuptake Inhibitor (SSRI) anti-depressants (e.g. Prozac) 21 days prior to starting ABT-263
• Must have adequate bone marrow, renal and hepatic function per local laboratory reference range as follows: ANC >= 1000/microL, Platelets >= 75,000/mm³ (entry platelet count must be independent of transfusion within 14 days of Screening), Hemoglobin >= 9.0 g/dL, Serum creatinine <= 2.0 mg/dL or calculated creatinine clearance >= 50 mL/min, AST and ALT <= 3.0 x ULN of institution's normal range, Bilirubin <=1.5 x ULN, Gilbert's Syndrome patients may have a Bilirubin > 1.5 x ULN, Coagulation: aPTT, PT must not exceed 1.2 x ULN;
• Surgically sterile or postmenopausal (for at least 1 year), or a negative pregnancy test performed as follows: At Screening on a serum sample obtained within 14 days prior to initial study drug administration, and prior to dosing on a urine sample obtained on Day 1 if it has been > 7 days since obtaining the serum pregnancy test results
• All female subjects not surgically sterile or postmenopausal (for at least 1 year) and non-vasectomized male subjects must practice at least one of the following methods of birth control: total abstinence from sexual intercourse (minimum 1 complete menstrual cycle); a vasectomized partner; hormonal contraceptives (oral, parenteral or transdermal) for at least three months prior to study drug administration; double-barrier method (including condoms, contraceptive sponge, diaphragm or vaginal ring with spermicidal jellies or cream)
• Voluntarily sign and date informed consent, approved by an Independent Ethics Committee (IEC)/Institutional Review Board (IRB), prior to the initiation of any screening or study-specific procedures.

Exclusion Criteria:

• Has a history or is clinically suspicious for cancer-related CNS disease
• Recent history (within 1 year prior to 1st dose of study drug) of an underlying, predisposing condition of bleeding or exhibits signs of bleeding
• Allogeneic or autologous stem cell transplant
• Active peptic ulcer disease or other potentially hemorrhagic esophagitis/gastritis
• Active immune thrombocytopenic purpura or history of being refractory to platelet transfusions (within 1 year prior to 1st dose of study drug)
• Receiving or requires anticoagulation therapy or any drugs or herbal supplements that effect platelet function, with the exception of low dose anti-coagulation meds used to maintain the patency of a central intravenous catheter
• Received aspirin within 7 days prior to 1st dose of study drug
• Received steroid therapy within 7 days prior to the 1st dose of study drug with the exception of inhaled steroids for asthma, topical steroids, or replacement/stress corticosteroids
• Received anti-cancer therapy including chemotherapy, immunotherapy, radiotherapy, hormonal (with the exception of hormones for thyroid conditions or estrogen replacement therapy (ERT), or any investigational therapy within 28 days prior to 1st dose of study drug
• Has received a biologic within 30 days prior to 1st dose of study drug
• Significant history of cardiovascular, renal, neurologic, psychiatric, endocrinologic, metabolic, immunologic, or hepatic disease that would adversely affect his/her participating in this study
• Female is pregnant or breast-feeding
• Tested positive for HIV
• Previous or current malignancies at other sites, with the exception of: adequately treated in situ carcinoma of the cervix uteri; basal or squamous cell carcinoma of the skin; previous malignancy (e.g., localized prostate cancer) confined and surgically resected with no evidence of disease within three years
• Exhibits evidence of other clinically significant uncontrolled condition(s) including, but not limited to: uncontrolled systemic infection (viral, bacterial, or fungal); diagnosis of fever and neutropenia within 1 week prior to study drug administration