During Course 2, participants whose leukemia expresses CD20 will receive rituximab by infusion over 4 hours on Days 1 and 8. Other participants who do not have CD20 on the leukemia cells will start with methotrexate by vein over 24 hours on Day 1. Cytarabine (ara-C) will be given by vein over 2 hours every 12 hours for 4 doses (Days 2 and 3). Vincristine will be given by vein over 15 to 30 minutes on Days 1 and 8. Pegylated asparaginase will be given by vein over 30 minutes on Day 4 or 5 after the methotrexate has cleared (as checked by blood tests).