Chronic graft versus host disease (cGVHD) can affect people who had a hematopoietic stem cell transplant using donor cells. It is often fatal. It is usually treated with high doses of steroids. But that helps only about half the people in the long term. Researchers want to see if a drug called baricitinib can help people with cGVHD that has not responded to therapy. The drug inhibits the proteins involved in communication in the immune system. These proteins may play a role in cGVHD and other inflammatory diseases.