Participants in this research study have been newly diagnosed with advanced (Stage III or IV) classical Hodgkin lymphoma (HL) (a cancer of the lymph nodes) and have not received any treatment for the disease. Participants will receive one of two regimens, either a regimen that includes an investigational drug called brentuximab vedotin (also known as ADCETRIS®) (this regimen/group is referred to as Arm A) or a commonly prescribed regimen (this regimen/group is referred to as Arm B). ADCETRIS has been approved in the United States by the Food and Drug Administration (FDA) for treatment of some types of lymphoma in patients where other therapies have failed. The use of ADCETRIS in this study is experimental, which means that the drug has not been approved by the FDA for use in patients that have not received any treatment for their HL (also known as frontline therapy). The main purpose of this study is to measure how well treatment in Arm A works compared to treatment in Arm B for HL. Approximately 1,040 patients at approximately 150 centers worldwide will participate in this study.