OBJECTIVES: I. Determine the anticancer efficacy of 506U78 in patients with chronic lymphocytic leukemia refractory to fludarabine and alkylator therapy. II. Determine the safety (including incidence of infection) of this drug in these patients. III. Evaluate the pharmacokinetics of 506U78 and ara-G, and assess the intracellular pharmacokinetics of ara-GTP in patients receiving multiple treatment courses (at M.D. Anderson Cancer Center only). IV. Determine the response rate, time to maximal response, and duration of response in patients treated with this drug. V. Determine two-year survival and progression-free survival of patients treated with this drug.