This is an open-label study (patients and study staff will know the identity of treatments assigned during the study) in patients with chronic graft-versus-host disease (cGvHD). Chronic graft-versus-host disease (a donator-versus-recipient-disease) is a complication that can occur after a blood stem cell or bone marrow transplant with cells from a related or unrelated donator. During cGvHD, the transplanted cells attack the recipient's body. Patients with cGVHD who meet entry criteria for the study will be randomly assigned to receive standard of care treatment for 26 weeks or standard or care treatment with extracorporeal photopheresis (ECP) for 26 weeks. Standard of care treatment consists of orally (taken by mouth) administered corticosteroids (drugs that reduce inflammation) and cyclosporine (CsA)or Tacrolimus ( drugs that suppress the patient's immune response). ECP therapy is a process that takes place in a device where the investigational drug UVADEX (methoxsalen) is injected into a germ-free bag mixed with the patient's white blood cells. After the blood cells have absorbed the drug and are exposed to ultraviolet A (UVA) radiation, the blood cells are injected back into the patient's body. During the study, a third party assessor at each study center who will be blinded (will not know) to treatment will assess the condition each patient's skin and oral mucosa at protocol-specified visits and will complete a total skin score for all patients . The study will consist of 3 phases: a screening phase, an open label treatment phase and an end-of-study (or early withdrawal) phase. The duration of patient participation will be 28 weeks and patient safety will be monitored throughout the study. An additional non-interventional 2 year follow-up will begin after the 28 week/withdrawal end-of-study phase.