This is an open label, Phase I/II, dose escalation research study of an investigational product called lumiliximab, given with FDA (Food and Drug Administration) approved products fludarabine, cyclophosphamide, and rituximab (FCR). The study duration is 17 visits over 42 months or until your disease progresses and you require additional CLL therapy. The total duration of participation in the study will be approximately 4 years, however your disease status will be followed indefinitely (forever).

Inclusion Criteria:

• Age: 18 years and older
• Diagnosis of B-cell CLL by International Workshop on CLL (IWCLL) response criteria
• Relapsed CD23+ B-cell CLL
• Rai Stage III or IV, or Rai Stage I or II if determined to have disease progression as evidenced by rapid doubling or peripheral lymphocyte count, progressive lymphadenopathy, progressive splenomegaly, or B symptoms
• Prestudy WHO Performance Status less than or equal to 2
• Signed, written Institutional Review Board (IRB)-approved informed consent
• Men & women of reproductive potential must agree to follow accepted birth control methods during treatment for 3 months after completion of treatment
• Acceptable liver function: Bilirubin less than or equal to 2.0 mg/dL (26 µmol/L), AST (SGOT) &/or ALT (SGPT) less than or equal to 2 times upper limit of normal
• Acceptable hematologic status: Platelet count less than or equal to 50 x 10^9/L, ANC less than or equal to 1 x 109/L
• Acceptable renal function: Serum creatinine less than or equal to 1.5 times upper limit of normal

Exclusion Criteria:

• Subjects who did not respond to prior FCR therapy (relapsed within 6 months of the last dose).
• Cancer radiotherapy, radioimmunotherapy, biological therapy, chemotherapy, or other investigational therapy within 4 weeks prior to Study Day 1
• Previous exposure to lumiliximab or other anti-CD23 antibodies
• Subjects who have had a prior allogenic bone marrow transplant (BMT) or autologous BMT or peripheral stem-cell transplant (PBSCT)
• Known infection with HIV, hepatitis B, or hepatitis C
• Uncontrolled diabetes mellitus
• Uncontrolled hypertension
• Transformation to aggressive B-cell malignancy (e.g., larger B-cell lymphoma, Richter's Syndrome, or prolymphocyte leukemia (PLL)
• Subjects with secondary malignancy requiring active treatment (except hormonal therapy)
• Subjects with medical conditions currently requiring long-term use (less than 1 month) of systemic corticosteroids
• Serious nonmalignant disease or laboratory abnormality, which, in the opinion of the investigator &/or sponsor, would compromise protocol objectives
• Active uncontrolled bacteria, viral, or fungal infections
• New York Heart Association Class III or IV cardiac disease, myocardial infarction within the past 6 months prior to Study Day 1, unstable arrhythmia, or evidence of ischemia on ECG within 14 days prior to Study Day 1
• Seizure disorders requiring anticonvulsant therapy
• Severe chronic obstructive pulmonary disease with hypoxemia
• Major surgery, other than diagnostic surgery, within 4 weeks prior to Study Day 1
• Clinically active autoimmune disease
• Subjects with a history of fludarabine-induced autoimmune cytopenia
• Pregnant or currently breast-feeding