The purpose of this research study is to determine the effectiveness and safety of Avastin when combined with standard chemotherapy for Hodgkin lymphoma. Avastin works differently than standard chemotherapy drugs. It is a type of protein called an antibody which binds to a substance called VEGF(Vascular Endothelial Growth Factor). VEGF stimulates the growth of the blood vessels that feed tumors and encourages tumor cell growth. VEGF is produced in excess by Hodgkin lymphoma cells, and is associated with a poorer outcome in patients with Hodgkin lymphoma. When the activity of VEGF is interrupted in multiple other cancer types, the blood vessels around the tumor cells die resulting in less nutrient delivery and death to the tumor. Blocking of VEGF has also been shown to improve delivery of chemotherapy to cancer cells, making standard chemotherapy work better. This trial uses Avastin in combination with standard chemotherapy with the goal of improving the cure rate over chemotherapy alone.