Study Assessing the Safety and Efficacy of ABT-263 in Subjects With B-cell Chronic Lymphocytic Leukemia (CLL) Who Have Failed at Least One Prior Fludarabine-containing Regimen

Inclusion Criteria: * \>= 18 yrs of age, have B-cell CLL, failed at least 1 prior fludarabine-containing regimen. * Refractory to 1 fludarabine-containing regimen is defined as failure to achieve at least PR to the last fludarabine-containing regimen received, or disease progression while receiving the last fludarabine-containing regimen, or disease progression in responders (i.e., achieved a PR or CR) within 6 mos of the last cycle of the last fludarabine-containing regimen received (e.g., fludarabine monotherapy, FR, or FC) or in responders (i.e., achieved a PR or CR ) within 24 mos of the last cycle of FCR. * Intolerant to fludarabine is defined as discontinuation of therapy within 2 cycles due to side effects/toxicity from the last fludarabine-containing regimen. * ECOG score of \<=1. * Adequate coagulation, renal, \& hepatic function at Screening as follows: * Serum creatinine \<= 2.0 mg/dL or calculated creatinine clearance \>= 50 mL/min; * AST \& ALT \<= 3.0 x ULN; * Bilirubin \<= 1.5 x ULN. * Gilbert's Syndrome may have a Bilirubin \> 1.5 x ULN; aPTT, PT, not to exceed 1.2 x ULN. * Adequate bone marrow (BM) independent of any growth factor support (with the exception of subjects with BM heavily infiltrated with underlying disease \[80% or more\] who may use growth factor support to achieve adequate BM) at Screening as follows: * ANC \>= 1000/µL; * Platelets \>= 75,000/mm3 (entry platelet count must be independent of transfusion within 14 days of Screening); * Hemoglobin \>= 9.0 g/dL. * History of autologous BM transplant must be \> 6 mos post transplant (prior to the 1st dose of study drug) \& have adequate BM independent of any growth factor support (with the exception of subjects with BM that is heavily infiltrated with underlying disease \[80% or more\] who may use growth factor support to achieve adequate BM) at Screening as follows: * ANC \>= 1500/µL; * Platelets \>= 125,000/mm3; * Hemoglobin \>= 10.0 g/dL. * Female subjects must be surgically sterile, postmenopausal (at least 1 year), or have negative results on a pregnancy test. * All female subjects not surgically sterile or postmenopausal (at least 1 year) \& non-vasectomized male subjects must practice birth control. Exclusion Criteria: * History/clinically suspicious for cancer-related CNS disease. * Undergone allogeneic stem cell transplant. * Undergone autologous stem cell transplant w/i 6 mos prior to 1st dose. * History/predisposing condition of bleeding or currently exhibits signs of bleeding. * Recent history of non-chemotherapy induced thrombocytopenic associated bleeding w/i 6 mos prior to 1st dose. * Active peptic ulcer disease or other hemorrhagic esophagitis/gastritis. * Active immune thrombocytopenic purpura or history of being refractory to platelet transfusions w/i 1 yr prior to 1st dose. * Currently receiving/requires anticoagulation therapy or any drugs or herbal supplements that affect platelet function, with the exception of low-dose anticoagulation medications used to maintain the patency of a central IV catheter. * Significant history of cardiovascular disease, renal, neurologic, psychiatric, endocrinologic, metabolic, immunologic, or hepatic disease. * Positive for HIV, Hepatitis B, or Hepatitis C. * Previous or current malignancies w/i the last 3 yrs: * except adequately treated in situ carcinoma of the cervix uteri; * basal or squamous cell carcinoma; * in situ carcinoma of the bladder; * or previous malignancy confined and surgically resected with curative intent. * Has Prolymphocytic leukemia or Richter's transformation to an aggressive B-cell malignancy. * Exhibits evidence of other clinically significant uncontrolled condition(s) including, but not limited to uncontrolled systemic infection or diagnosis of fever and neutropenia w/i 1 week prior to study drug. * Prior exposure to ABT-263. * Received antibody therapy w/i 30 days prior to 1st dose. * Received any anti-cancer therapy including chemotherapy, immunotherapy, radiotherapy, hormonal, or any investigational therapy w/i 14 days prior to the 1st dose, or has not recovered to \<Gr2 clinically significant AE(s) /toxicity(s) of the previous therapy. * Received steroid therapy for anti-neoplastic intent, w/i 7 days prior to the 1st dose with the exception of inhaled steroids for asthma, topical steroids, or replacement/stress corticosteroids. * Received aspirin w/i 7 days prior to the 1st dose. * Consumed grapefruit or grapefruit products w/i 3 days prior to 1st dose. * Females pregnant or breast-feeding.