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.