Treatment will be given on an outpatient basis. The treatment can be given at M. D. Anderson or by your local cancer doctor. Patients who are assigned to the rituximab arm must be willing to get their first and third cycle (all 4 doses) at M. D. Anderson, if their local physician is unable to draw and ship samples to the central laboratory for rituximab levels. Blood will be drawn (approximately one teaspoon) before and after the first and fourth dose and before the second and third dose of those two treatment cycles. The treatment will be given by vein over a period of several hours. Participants who have easily accessible veins may get this treatment by having a temporary needle placed in the vein for the treatment. For participants who do not have easily accessible veins, a central venous catheter (long plastic tube - CVL) will be placed in a big vein of the arm or chest.