 If you are found to be eligible to take part in this study, you will be given the study drugs in 21-day cycles. The cycles will alternate between R-HCVAD and a combination of rituximab, methotrexate, and Ara-C. During Cycle 1 the R-HCVAD cycle, you will receive rituximab through a needle in your vein intravenously, or IV, on Day 1. The infusion will take about 1 hour. Cyclophosphamide will be given by IV every 12 hours for 3 days. Each infusion of cyclophosphamide will take about 3 hours. Doxorubicin will be given as a 15-minute infusion on Day 5 with the supervision of a nurse. Your doctor may also choose to give you the doxorubicin over 24-48 hours using a small pump that you will carry around your waist in a fanny pack. You will not have to stay in the hospital to receive this study drug. Vincristine will be given by IV, on Days 5 and 12. Each vincristine infusion will take about an hour. Dexamethasone will be given by mouth as a pill, capsule, or tablet on Days 2-5 and 12-15. You will also be given other standard medications to help prevent possible side effects of these medications such as nausea, vomiting, or rash. 