OBJECTIVES: I. Determine the overall response rate of previously untreated patients with stage I, II, III, or IV B-cell chronic lymphocytic leukemia when treated with fludarabine induction followed by alemtuzumab consolidation. II. Determine the infectious toxic effects and feasibility of this regimen in this patient population. III. Determine the treatment-related toxic effects, including infection and injection site reactions, of subcutaneous vs intravenous alemtuzumab in patients treated with this regimen. IV. Determine the progression-free and overall survival of patients treated with this regimen. V. Determine the immunologic effects of this regimen in these patients.