Inclusion Criteria:A. Subject has cGVHD requiring systemic therapy occurring >100 days after hematopoietic cell transplant diagnosed with at least one diagnostic feature from Appendix A.

B. Subject has active cGVHD with either:

1. Persistent steroid dependence defined as the inability to taper steroid treatment to less than 0.25 mg/kg/d prednisone or its equivalent for at least 3 months
2. Progression of cGVHD signs and symptoms on steroid therapy equivalent to prednisone 0.5 mg/kg/d for at least 1 month.

C. Subject has at least one of the following manifestations with which to follow progression of disease or response to imatinib:

1. Skin changes (rash, sclerosis, fasciitis, or ulceration)
2. Abnormal eye wetness <= 5 mm as measured by Schirmer's test
3. Oral mucosal changes (erythema, lichenoid changes, ulcers, or mucoceles)
4. Thrombocytopenia (platelets <150,000/uL).
5. Abnormal liver function testing (alkaline phosphatase, AST, ALT, or total bilirubin > ULN).
6. Bronchiolitis obliterans (diagnosed by a > 5% annual decline in FEV1 with the lowest post-transplant FEV1/FVC < 0.8 and an appropriate CT scan or lung biopsy, see Appendix A for details)

D. Subject may have previously any received immunosuppressive therapies for cGVHD. Continuing treatment with steroids and any one or none of the following is allowed: cyclosporine, tacrolimus, sirolimus, mycophenolate mofetil, or extracorporeal photopheresis.

E. Subject has been on a fixed dose of steroids or a fixed dose of steroids and one other immunosuppressant (cyclosporine, tacrolimus, sirolimus, mycophenolate mofetil, or extracorporeal photopheresis) for >= 30 days before starting imatinib.

F. Subject has a life expectancy >= 6 months.

G. Subject has the ability to understand and willingness to sign a written informed consent document.

H. Subject has a Karnofsky performance status^3 50% (Appendix B).

I. Subject is ³ 18 years of age.

J. If a female with reproductive potential (defined as having at least 1 menstrual period in the past 12 months), the subject must have a negative pregnancy test performed <= 7 days before starting study drug.

K. If a female with reproductive potential, the subject agrees to use contraception for the duration of the trial.

L. Subject has a total bilirubin < 1.5X ULN.

M. Subject has an aspartate transaminase (AST), alanine aminotransferase (ALT), and alkaline phosphatase < 2.5X ULN.

N. Subject has an absolute neutrophil count > 500/uL (growth factor supplementation is allowed).

O. Subject has a hematocrit > 26% (transfusion support is allowed).

P. Subject has a platelet count > 20,000/uL.&#xA; Exclusion Criteria:A. Subject has received another investigational agent <= 30 days before starting the study drug.

B. Subject has an on-going, intercurrent illness such as an infection not responsive to antibiotics, antiviral medicines, or antifungal medicines.

C. Subject has progressive malignant disease.

D. Subject has a secondary malignancy that has not been effectively treated within the past 5 years (except localized basal cell or squamous cell carcinoma).

E. Subject has imatinib intolerance or allergy.

F. Subject is breast-feeding.

G. Subject is not willing to comply with treatment or response evaluation.

H. Subject has received an allogeneic cell product (including DLI or hematopoietic cell boost) <= 100 days before starting study drug.

I. The subject's steroid and/or immunosuppressant dose has changed <= 30 days before starting study drug.