Lumiliximab With Fludarabine, Cyclophosphamide, and Rituximab (FCR) Versus FCR Alone in Subjects With Relapsed Chronic Lymphocytic Leukemia (CLL)

Inclusion Criteria: * Signed, written EC-approved informed consent form. * Diagnosis of relapsed CD23+ and CD20+ B cell CLL as defined by NCI WG guidelines. * Subjects who have received at least 1 but no more than 2 prior single agent or combination treatments for CLL. * Rai Stage III or IV (Binet Stage C), or Rai Stage I or II (Binet Stage A or B) if determined to have disease progression as evidenced by rapid doubling of peripheral lymphocyte count, progressive lymphadenopathy, progressive splenomegaly, or B symptoms (Staging Criteria - Modified Rai). * WHO Performance Status less than or equal to 2. * Age greater than or equal to 18 years. * Male and female subjects of reproductive potential must agree to follow accepted birth control methods during treatment and for 12 months after completion of treatment. * Acceptable liver function: bilirubin less than or equal to 2.0 mg/dL (26 µmol/L); AST and ALT less than or equal to 2 times upper limit of normal. * Acceptable hematologic status: platelet count greater than or equal to 50 x 10\^9/L should be unsupported by transfusion; ANC greater than or equal to 1 x 10\^9/L. * Acceptable renal function: creatinine clearance calculated according to the formula of Cockcroft and Gault \>50 mL/min; serum creatinine less than or equal to 1.5 times upper limit of normal. Exclusion Criteria: * Subjects who are refractory to the following combination therapies: purine analogue + R, purine analogue + C, or purine analogue + CR. Refractory is defined as not achieving at least a PR for a minimum duration of 6 months as determined by treating physician. Purine analogues include fludarabine, pentostatin and cladribine. * 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. * Prior autologous or allogeneic BMT or hematopoetic stem cell transplant. * Known infection with HIV, hepatitis B, or hepatitis C. Although testing for hepatitis B or hepatitis C is not mandatory, this should be considered for all subjects considered at high risk of hepatitis B or hepatitis C infection and in endemic areas. Subjects with any serological evidence of current or past hepatitis B or hepatitis C exposure are excluded unless the serological findings are clearly due to vaccination. * Uncontrolled diabetes mellitus. * Uncontrolled hypertension. * Transformation to aggressive B-cell malignancy (e.g., large B cell lymphoma, Richter's Syndrome, or PLL). * Secondary malignancy requiring active treatment (except hormonal therapy). * Any medical condition that would require long-term use (\>1 month) of systemic corticosteroids during study treatment. However, steroid use less than or equal to 1 month is permissible during the study. * Any serious nonmalignant disease or laboratory abnormality, which in the opinion of the Investigator and/or Sponsor would compromise protocol objectives. * Active uncontrolled bacterial, 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 30 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. * History of fludarabine-induced autoimmune cytopenia (as judged by the Investigator) or Coombs-positive haemolytic anemia. * Pregnant or currently breastfeeding.