Study of ABT-263 When Administered in Combination With Either Fludarabine/Cyclophosphamide/Rituximab or Bendamustine/Rituximab in Relapsed or Refractory Chronic Lymphocytic Leukemia

* Must have relapsed or refractory Chronic Lymphocytic Leukemia (CLL), received no more than 5 prior myelosuppressive/chemotherapy regimens and must be a candidate for treatment with either Fludarabine/Cyclophosphamide/Rituximab (FCR) or Bendamustine/Rituximab (BR); * Subject has an Eastern Cooperative Oncology Group (ECOG) performance score of \/=1000/mcL, Platelets\>/= 100,000/mm3 (entry platelet count must be independent of transfusion within 14 days of Screening),Hemoglobin \>/= 9.0 g/dL.

* Subject has history or is clinically suspicious for cancer-related Central Nervous System disease; * Has history of severe allergic or anaphylactic reactions to human, humanized, chimeric or murine monoclonal antibodies; * Has undergone an allogeneic stem cell transplant; Exhibits evidence of other uncontrolled condition(s) including, but not limited to: uncontrolled systemic infection, diagnosis of fever and neutropenia within 1 week prior to study drug administration; * Has underlying, predisposing condition of bleeding or currently exhibits signs of bleeding; Has a recent history of non-chemotherapy induced thrombocytopenic associated bleeding; * Currently receiving or requires anticoagulation therapy; * Has active immune thrombocytopenic purpura (ITP) or a history of being refractory to platelet transfusions (within 1 year prior to 1st dose of study drug); * Has active peptic ulcer disease or other hemorrhagic esophagitis/gastritis.