Inclusion Criteria:

          -  Men and women: ≥ 65 years of age OR > 18 and < 65 years of age, provided that they
             meet at least one of the following criteria:

               1. Creatinine clearance 30 to 69 mL/min.

               2. A score higher than 6 on the Cumulative Illness Rating Scale-Geriatric.

          -  ECOG performance status of 0, 1, or 2.

          -  Diagnosis of CD20+ CLL.

          -  Active disease meeting ≥ 1 of the following IWCLL 2008 criteria for requiring
             treatment.

          -  Meet the following laboratory parameters:

               1. ANC ≥ 750 cells/μL, or ≥ 500 cells/μL in subjects with documented bone marrow
                  involvement, and independent of growth factor support 7 days before assessment.

               2. Platelet count ≥ 50,000 cells/μL, or ≥ 30,000 cells/μL in subjects with
                  documented bone marrow involvement, and without transfusion support 7 days before
                  assessment. Subjects with transfusion-dependent thrombocytopenia are excluded.

               3. Serum AST and ALT/SGPT ≤ 3.0 x ULN.

               4. Total bilirubin ≤ 1.5 x ULN.

               5. Estimated creatinine clearance ≥ 30 mL/min.

        Exclusion Criteria:

          -  Any prior systemic treatment for CLL.

          -  Known CNS lymphoma or leukemia.

          -  Known prolymphocytic leukemia or history of, or currently suspected, Richter's
             syndrome.

          -  Uncontrolled autoimmune hemolytic anemia or idiopathic thrombocytopenia purpura.

          -  Major surgery within 4 weeks before first dose of study drug.

          -  Prior malignancy, except for adequately treated lentigo maligna melanoma,
             non-melanomatous skin cancer, in situ cervical carcinoma, or other malignancy treated
             with no evidence of active disease > 3 years before Screening and at low risk for
             recurrence.

          -  Significant cardiovascular disease within 6 months of screening.

          -  Known history of infection with HIV.

          -  History of stroke or intracranial hemorrhage within 6 months before randomization.

          -  Known history of a bleeding diathesis.

          -  Requires or receiving anticoagulation with warfarin or equivalent vitamin K
             antagonists within 7 days of first dose of study drug.