This study is designed to expand on the highly successful combination of rituximab, fludarabine and cyclophosphamide for patients with previously untreated CLL. Responses in the range of 90-98% with 55% complete responses are reported. However, bone marrow toxicity has been a significant problem. This trial is designed to reduce the bone marrow toxicity by decreasing the doses of fludarabine and cyclophosphamide, but doubling the dose of rituximab with a maintenance dose of rituximab for up to two years, to maintain or even enhance efficacy.