Patients 18 years of age and older with CLL who have CD25 receptor proteins on their cancer cells and whose disease has progressed within 2 years of treatment with fludarabine may be eligible for this study. Candidates are screened with a medical history and physical examination, blood and urine tests, electrocardiogram (EKG), echocardiogram, chest x-ray, computed tomography (CT) scans of the chest, abdomen and pelvis, and a bone marrow biopsy.