This trial is testing ibrutinib, a pill that blocks a protein causing harmful immune reactions, in adults with newly diagnosed moderate or severe chronic graft-versus-host disease (cGVHD). The goal is to see if this drug can help control the disease by reducing the immune system's attack on the body. Ibrutinib was the first agent approved by the U.S. Food and Drug Administration for the treatment of chronic graft-versus-host disease (cGVHD) after failure of one or more lines of systemic therapy.