This study will determine if a dexamethasone mouth rinse can reduce the risk of developing oral chronic graft-versus-host disease (cGVHD) in patients who have undergone a bone marrow (stem cell) transplant procedure. cGVHD is a common complication of stem cell transplantation, resulting from the donor cells attacking the transplant recipient's tissues. In oral cGVHD, the tissues in the mouth are damaged, causing painful mouth sores. Dexamethasone is a corticosteroid that is commonly used to treat inflammation. It is the only corticosteroid available that can be used as a mouth rinse.