This study will examine the safety and effectiveness of extracorporeal photopheresis (ECP) for treating chronic graft-versus-host disease (GvHD). GvHD is a common complication of stem cell transplantation using donated stem cells. It occurs when the donor's T-lymphocytes (a type of immune cell) see the patient's cells as foreign and mount an immune response to reject them. The attack can cause skin rash, mouth sores, liver or lung inflammation, lack of appetite, and muscle stiffness. Chronic GvHD can cause serious illness, and even death, from the long-term effects of immune dysfunction and from toxic effects of medications (such as cyclosporine and prednisone) used to treat it.