Inclusion Criteria:

- Previously untreated histologically or cytologically documented B-cell non-Hodgkin's
lymphoma; the following histologies are eligible: diffuse large B-cell lymphoma,
high-grade large cell immunoblastic lymphoma, anaplastic large cell lymphoma,
Burkitt's lymphoma, high-grade B-cell lymphoma, Burkitt-like (small non-cleaved
lymphoma)

- Tumors must be CD20 positive

- Documented HIV infection: documentation may be serologic (ELISA, western blot),
culture, or quantitative PCR or bDNA assays

- Evaluable or measurable disease

- Stage I and IE or Stage II-IV disease patients

- ANC >= 1000 cells/mm^3

- Platelet count >= 75,000/mm^3 unless cytopenias are secondary to lymphoma

- All patients must be off colony stimulating factor therapy at least 24 hours prior to
chemotherapy

- Transaminase =< 5 times the upper limit of normal unless secondary to hepatic
infiltration with lymphoma or isolated hyperbilirubinemia associated with the use of
indinavir or other antiretrovirals

- Total Bilirubin < 2.0 unless secondary to hepatic infiltration with lymphoma or
isolated hyperbilirubinemia associated with the use of indinavir or other
antiretrovirals; for bilirubin > 3.0 due to hepatic involvement the initial dose of
doxorubicin will be decreased by 50% and the initial dose of vincristine will be
omitted

- Creatinine < 2.0 unless due to lymphoma

- KPS >= 50 (ECOG PS 0, 1, or 2)

- Able to give consent

- Female patients must have a negative pregnancy test within 72 hours of entering into
the study; males and females must agree to use adequate birth control if conception
is possible during the study; women must avoid pregnancy and men avoid fathering
children while in the study

- Patients already receiving erythropoeitin or G-CSF are eligible

- Patients must have a left ventricular ejection fraction that is at or above the lower
institutional limits of normal, as assessed by nuclear scan or echocardiogram
obtained within 12 weeks of registration

- Lymphomatous meningitis (patients with a positive CSF cytology are eligible)

Exclusion Criteria:

- Previous chemotherapy or radiotherapy for this lymphoma

- Primary Central Nervous System Lymphoma (parenchymal brain or spinal cord tumor)

- Acute active HIV-associated opportunistic infection requiring antibiotic treatment;
patients with mycobacterium avium are not excluded; chronic therapy with potentially
myelosuppressive agents is allowed provided that entry hematologic criteria are met

- Concurrent malignancy (excluding in situ cervical cancer, or non-metastatic
non-melanomatous skin cancer, or Kaposi's sarcoma not requiring systemic
chemotherapy)

- Previous therapy with rituximab within 12 months; patients treated with rituximab
more than 12 months earlier are eligible only if it was given for indications other
than the treatment of intermediate- or high-grade lymphoma (eg, low-grade lymphoma or
ITP)