Inclusion Criteria:

• B-CLL patients with refractory or relapsed disease who have received one or more prior lines of treatment which must have included either a fludarabine based regimen or an alkylator based regimen.
• Diagnosis of B-CLL according to NCI Working Group Criteria.
• Have an elevated B-cell count of ≥ 5000/mm3.
• Have a T-cell count ≥ 200/mm3.
• ECOG Performance Status ≤ 2.
• Have a life expectancy of at least 3 months.
• Age > 18 years, of either gender.
• Have given written informed consent, prior to any study related procedure not part of the patient's normal medical care

Exclusion Criteria:

• Patients who, in the opinion of the Investigator, need immediate treatment with proven chemotherapy and/or immunotherapy, and/or transplantation.
• Have B-CLL with central nervous system involvement.
• Have participated in any other investigational drug study or have undergone an experimental therapeutic procedure considered to potentially interfere with the study in the 30 days preceding Day 1.
• Have received chemotherapy or radiotherapy treatment in the 30 days preceding Day 1.
• Require oral or parenteral steroids with the exception of inhaled steroids or low-dose oral steroids (<10mg prednisolone per day or equivalent) for an indication other than B-CLL.
• Have a serious medical or psychiatric condition that could, in the Investigator's opinion, potentially interfere with their treatment and/or participation in the study.
• Have uncontrolled diabetes mellitus that requires insulin treatment or is not controlled on oral therapy.
• Have a history of gout.

• Have a serious concomitant disease including:

  • Significant cardiac disease - New York Heart Association Classes III or IV or have suffered a myocardial infarction in the last 6 months.
  • Chronic pulmonary obstructive disease with hypoxemia.
  • Clinically active auto-immune disease.
  • Active infection such as tuberculosis, CMV (Cytomegalovirus).
• Any secondary malignancy requiring active treatment (except hormonal therapy).
• Have inadequate bone marrow reserve: neutrophils < 1.0 x 109/L, platelet count < 50 x 109/L (unsupported by transfusion), or coagulation abnormalities.
• Have inadequate liver function: total bilirubin > 1.5 x upper limit of normal values (ULN), AST, ALT, or alkaline phosphatase > 2.5 x ULN.
• Have inadequate renal function, defined by serum creatinine ≥ 1.5 x ULN, unless creatinine clearance is measured and found to be at least 60 mL/min.
• Have serum uric acid levels outside the normal range.
• Females of childbearing potential who are unwilling to employ adequate means of contraception (hormonal contraceptive, intrauterine device, diaphragm with spermicide or condom with spermicide) for the duration of the study and 30 days after the last acadesine administration.
• Pregnant or lactating females.
• Male patients who are not surgically sterile and who are unwilling to use a condom with spermicide for the duration of the study and for 3 months after the last acadesine administration.
• Abuse of alcohol or other recreational drugs.
• Known HIV or Hepatitis B (unless clearly due to vaccination) or C positive.
• Known allergy to acadesine or any of its excipients.
• Have undergone previous allogeneic stem cell transplant.
• Transformation to Richter's syndrome or other aggressive B-cell malignancy