• The primary study endpoint for the phase 3 portion of the study will be Progression Free Survival (PFS) rate. [ Time Frame: Every 3 months through month 48 ] [ Designated as safety issue: No ]
  
• Complete Response (CR) rate is the efficacy endpoint for the phase 2 portion of the study. [ Time Frame: Every 3 months through month 48 ] [ Designated as safety issue: No ]
  

• Complete response. [ Time Frame: Every 3 months until month 48 ] [ Designated as safety issue: No ]
  
• Time to event variables (duration of response, time to next therapy, time to progression and overall survival) [ Time Frame: Every 3 months until month 48 ] [ Designated as safety issue: No ]
  
• Response variables (complete response rate, overall response rate, partial response rate) [ Time Frame: Every 3 months until month 48 ] [ Designated as safety issue: No ]
  

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.