Randomized phase III trial to compare the effectiveness of combination chemotherapy with or without monoclonal antibody therapy in treating patients who have previously untreated HIV-associated non-Hodgkin's lymphoma. Drugs used in chemotherapy use different ways to stop cancer cells from dividing so they stop growing or die. Monoclonal antibodies such as rituximab can locate cancer cells and either kill them or deliver cancer-killing substances to them without harming normal cells. It is not yet known whether combination chemotherapy plus monoclonal antibody therapy is more effective than combination chemotherapy alone in treating HIV-associated non-Hodgkin's lymphoma.