This phase II trial studies how well combination chemotherapy with or without rituximab works in treating participants with stage III-IV classic Hodgkin lymphoma. Monoclonal antibodies, such as rituximab, may interfere with the ability of tumor cells to grow and spread. Drugs used in chemotherapy, such as doxorubicin hydrochloride, bleomycin, vinblastine, and dacarbazine, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving rituximab with combination chemotherapy may work better in treating participants with classic Hodgkin lymphoma.

PRIMARY OBJECTIVES:

I. To evaluate the event free survival (EFS) following therapy with rituximab plus adriamycin (doxorubicin hydrochloride), bleomycin, vinblastine, and dacarbazine (ABVD) or standard ABVD in patients with newly diagnosed classical Hodgkin lymphoma who have poor prognosis defined as International prognostic score (IPS) of > 2.

SECONDARY OBJECTIVES:

I. To compare the effect of the two treatment arms on positron emission tomography (PET) scan results after 2 cycles of therapy.

II. To compare the effect of the two treatment arms on the level of circulating malignant Hodgkin stem cells.

OUTLINE: Participants are randomized to 1 of 2 arms.

ARM A: Participants receive rituximab intravenously (IV) over 7 hours on days 1, 8, 15, and 22 of course 1 and on days 1 and 8 of course 2. Participants also receive doxorubicin hydrochloride, bleomycin, vinblastine, and dacarbazine IV over 1 hour on days 1 and 15. Treatment with ABVD repeats every 4 weeks for up to 6 courses in the absence of disease progression or unacceptable toxicity.

ARM B: Participants receive doxorubicin hydrochloride, bleomycin, vinblastine, and dacarbazine as in Arm A.

After completion of study treatment, participants are followed up every 3 months for the first year, every 4 months for the second year, every 6 months for years 3-5, and then annually thereafter.

Inclusion Criteria:

• Previously untreated patient with classical Hodgkin's lymphoma patients with stage III and IV
• International Prognostic Score of > 2 (patient must have > 2 of the following risk features: Male, >= 45 years of age, stage IV, albumin < 4, white blood cell count [WBC] >= 15, lymphocytes < 8% or < 600, hemoglobin [Hgb] < 10.5)
• Must sign a consent form
• Absolute neutrophil count (ANC) >= 1,500/microL
• Platelet > 100,000/microL
• Left ventricular ejection fraction (LVEF) >= 50% by multigated acquisition (MUGA) scan or echocardiogram
• Serum creatinine < 2 mg/dl
• Serum bilirubin < 2 mg/dl
• Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) < 2 x upper limit of normal (ULN)
• Bi-dimensionally measurable disease

Exclusion Criteria:

• Lymphocyte predominant Hodgkin's lymphoma
• Known human immunodeficiency virus (HIV) infection
• Pregnant women and women of child bearing age who are not practicing adequate contraception
• Prior chemotherapy or radiation therapy
• Severe pulmonary disease as judged by the principal investigator (PI) including chronic obstructive pulmonary disease (COPD) and asthma
• Active infection requiring treatment with intravenous therapy
• Presence of central nervous system (CNS) lymphoma
• Concomitant malignancies or previous malignancies within the last 5 years (exception made for adequately treated basal or squamous cell carcinoma of the skin or carcinoma in situ of cervix)
• Active hepatitis B or C infection