A Study of ABT-263 in Combination With Dose-Intensive Rituximab, or Dose-Intensive Rituximab Alone, in Previously Untreated Patients With B-Cell, Chronic Lymphocytic Leukemia (CLL)

Inclusion Criteria: * Previously untreated, CD20-positive B-cell CLL * ECOG performance status of 0 or 1 * Life expectancy \> 6 months * Willingness and capability to be accessible for follow-up until study termination or death * For patients of reproductive potential (both males and females), use of a reliable means of contraception Exclusion Criteria: * Prolymphocytic leukemia * Richter's transformation to an aggressive B-cell malignancy (e.g., DLBCL) * Prior radiotherapy to a lesion(s) that will be used to assess response unless that lesion(s) shows clear evidence of progression at baseline * Patients with a history of other malignancies within 2 years prior to study entry except for adequately treated carcinoma in situ of the cervix, basal or squamous cell skin carcinoma, low-grade, localized prostate cancer treated surgically with curative intent or one that carries a good prognosis, in situ ductal carcinoma of the breast treated with lumpectomy alone with curative intent * Prior treatment with rituximab, ABT-263 or other pro-apoptotic agents * Current or recent (within the 28 days prior to initiation of study treatment) participation in another experimental drug study * Major surgical procedure (excluding lymph node biopsy) or significant traumatic injury within 28 days prior to treatment onset or anticipation of the need for major surgery during the course of the study * Active infection requiring parenteral antibiotics or antiviral or antifungal agents at the onset of study treatment * Receipt of primary or booster vaccination with live-virus vaccines for up to 6 months prior to initiation of study treatment * Patients receiving therapeutic anticoagulation with heparin or warfarin or patients receiving any drugs or herbal supplements that are known to inhibit platelet function (including low-dose aspirin) within 7 days of the first dose of ABT-263. Note: Patients receiving low-dose anticoagulation for the purpose of maintaining central venous catheter patency are eligible. * Patients who have an inherited or acquired bleeding diathesis, including (but not limited to) hemophilia or immune or thrombotic thrombocytopenic purpura, or who have had an underlying condition that predisposes to abnormal bleeding (e.g., peptic ulcer disease) within 1 year prior to the first dose of ABT-263 * Patients with a history of refractoriness to platelet transfusions * Clinically significant cardiovascular disease * Known human immunodeficiency virus (HIV) infection, seropositivity for hepatitis B surface antigen (HBsAg) or hepatitis C virus (HCV) antibody or RNA * Pregnancy or breastfeeding * Concurrent (or within 7 days prior to the first dose of study treatment) systemic corticosteroid therapy except some low-dose corticosteroid therapies * History of other disease, metabolic dysfunction, physical or laboratory finding(s) giving reasonable suspicion of a disease or condition that contraindicates use of an investigational drug, might affect interpretation of the results of the study or render the patient at high risk from treatment complications * History of anaphylaxis, allergic reaction, or hypersensitivity to sulfites (sodium metabisulphite is included in study drug formulation) * Any contraindication to alcohol ingestion (study drug formulation includes approximately 15% ethanol)