Inclusion Criteria:

• Diagnosis of B-cell CLL
• Relapsed, fludarabine-sensitive (duration of response > 6 months as assessed by prior treating physician) or fludarabine-naive patients
• Rai Stage III or IV, or Rai Stage I or II if determined to have disease progression as evidenced by rapid doubling of peripheral lymphocyte count, progressive lymphadenopathy, progressive splenomegaly, or B symptoms.
• Prestudy WHO Performance Status </= 2.
• Signed, written IRB-approved informed consent.
• Men and women of reproductive potential must agree to follow accepted birth control methods during treatment and for 3 months after completion of treatment.
• Acceptable liver function: Bilirubin </= 2.0 mg/dL (26 umol/L), AST (SGOT) and/or ALT (SGPT) </= 2 times upper limit of normal.
• Acceptable hematologic status: Platelet count >/= 50 x 10^9/L., ANC >/= 1 x 10^9/L.
• Acceptable renal function: Serum creatinine </= 2.0 mg/dL

Exclusion Criteria:

• Cancer radiotherapy, radioimmunotherapy, biological therapy, chemotherapy, or other investigational therapy within 4 weeks prior to Study Day 1.
• Known infection with HIV, hepatitis B, or hepatitis C
• Transformation to aggressive B-cell malignancy (e.g., large B-cell lymphoma, Richter's Syndrome, or prolymphocyte leukemia [PLL]).
• Patients with secondary malignancy requiring active treatment (except hormonal therapy).
• Active uncontrolled bacterial, viral, or fungal infections.
• New York Heart Association Class II-IV cardiac disease or myocardial infarction within the past 6 months prior to Study Day 1.
• Pregnant or currently breast-feeding.
• Current, recent (within 4 weeks of the first infusion of this study), or planned participation in an experimental drug study other than a Genentech-sponsored bevacizumab cancer study.
• Blood pressure of > 150/100 mmHg
• Unstable angina
• History of stroke within 6 months
• Clinically significant peripheral vascular disease
• Evidence of bleeding diathesis or coagulopathy
• Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 1, anticipation of need for major surgical procedure during the course of the study.
• Minor surgical procedures, fine needle aspirations or core biopsies within 7 days prior to Day 1.
• Urine protein:creatinine ratio >/= 1.0 at screening.
• History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to Day 1.
• Serious, non-healing wound, ulcer, or bone fracture.