CC-4047 (Pomalidomide) for Graft vs. Host Disease

Patient must meet all of the following inclusion criteria: * Must be greater than or equal to 18 years of age at the time of consent. * Must be able to adhere to the study visit schedule and other protocol requirements. * Chronic graft versus host disease (GHVD) developing after allogeneic hematological stem cell transplantation diagnosed using NIH criteria for diagnosis and staging of chronic GvHD (including both "classic chronic GvHD" and "overlap syndrome") * Must have moderate or severe chronic GvHD according to Global Staging System for Chronic GvHD or mild chronic GvHD with platelet count less than 100 x 109/L * Must have failed to achieve response to high dose corticosteroid (average 0.5 mg/kg/day prednisone or equivalent for greater than or equal to 8 weeks), or have failed second line systemic immunosuppressive therapy. * If taking corticosteroids at the time of enrollment, must be on stable or tapering schedule without corticosteroid pulses in the preceding 8 weeks. * If taking secondary systemic immunosuppressive therapy at the time of enrolment, must be on stable or tapering schedule in the preceding 4 weeks. * Karnofsky performance score (KPS) greater than or equal to 60%. * Life expectancy greater than or equal to 3 months. * Female of childbearing potential (FCBP) must agree to use two reliable forms of contraception simultaneously or to practice complete abstinence from heterosexual intercourse for at least 28 days before starting study drug, while participating in the study, and for at least 28 days after discontinuation from the study. The two methods of reliable contraception must include one highly effective method (i.e. intrauterine device (IUD), hormonal \[birth control pills, injections, or implants\], tubal ligation, partner's vasectomy) and one additional effective (barrier) method (i.e. latex condom, diaphragm, cervical cap). FCBP must be referred to a qualified provider of contraceptive methods if needed. * FCBP must agree to pregnancy testing and contraceptive counseling every 28 days during the study. FCBP must also refrain from donating blood and/or egg while participating in the study and for at least 28 days after discontinuation from this study * FCBP must have two negative pregnancy tests (sensitivity of at least 25 mIU/mL) prior to starting study drug. The first pregnancy test must be performed within 10-14 days prior to the start of study drug and the second pregnancy test must be performed within 24 hours prior to the start of study drug. * Must agree to abstain from breastfeeding during study participation and for at least 28 days after study drug discontinuation. * Male Subjects must agree to complete abstinence or to use a condom during sexual contact with with a pregnant female or a female of childbearing potential while participating in the study and for at least 90 days following study drug discontinuation even if he has undergone a successful vasectomy * Must agree to counseling about sexual contact and the potential risks of fetal exposure to pomalidomide every 28 days. * Male subjects will be warned that sharing study drug is prohibited * Must agree to abstain from donating blood for at least 28 days following discontinuation of the study drug. * Must agree to abstain from donating semen or sperm during study participation and for at least 90 days after study drug discontinuation. * Must agree that if a pregnancy or a positive pregnancy test does occur in a the partner of a male study subject during study participation, the investigator must be notified immediately * Patients must agree to not share study drug with anyone during participation in the study. * Must understand and voluntarily sign an informed consent form, or must have a legally authorized representative who is able and willing to voluntarily sign an informed consent form on behalf of the patient. Exclusion Criteria: * Pregnant or lactating females. * New immunosuppressive therapy started within the preceding 4 weeks. * Extracorporeal photopheresis within the preceding 3 months. * Hypersensitivity to any immune modulator drug (IMiD™). * Unable to take prophylactic anticoagulation. * Any condition which places the patient at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study. * Acute, persistent, recurrent or late-onset acute GvHD defined by NIH criteria. * Any of the following laboratory values at registration: * absolute neutrophil count (ANC) less than 1.0 x 109/L, * platelets less than 75 x 109/L, or * creatinine clearance less than 50 mL/min (Cockroft-Gault formula). * Uncontrolled infection requiring systemic antibiotics. * Known human immunodeficiency virus (HIV), hepatitis B virus (HBV) and/or hepatitis C virus (HCV) infection. * Known uncontrolled arrhythmias or symptomatic heart disease or left ventricular ejection fraction less than 40% (an ECHO should be performed as clinically indicated) * Recurrence of cancer for which the transplant was done except for presence of minimal residual disease by PCR. * Other cancer less than or equal to 2 years prior study-entry except: * Basal cell carcinoma of the skin, * Squamous cell carcinoma of the skin, * Carcinoma in situ of the cervix, * Carcinoma in situ of the breast, or * Prostate cancer (Tumor, Node, Metastasis \[TNM\] stage T1a or T1b)