Brentuximab vedotin is an antibody that also has a chemotherapy drug attached to it. Antibodies are proteins that are part of the immune system. They can stick to and attack specific targets on cancer cells. The antibody part of brentuximab vedotin sticks to a target called CD30 that is located on the outside of the cancer cells. Normal cells have little or no CD30 on their surface. ATLL cancer cells often have a larger amount of CD30 on their surface than normal cells. However, CD30 is found in different amounts on ATLL cancer cells. This study will also test the amount of CD30 found on each participant's cancer cells. Researchers will be looking to see if the response to the study treatment varies based on the amount of CD30 found on the outside participants' cancer cells.