Patients on this study will receive stem cells from a related or an unrelated donor. The donor will be closely matched to the patients immune type but the donor is not a brother or sister. This type of transplantation has been done only a few times for patients with CGD, although this type of transplant is commonly done for other reasons, e.g. leukemia. The reason this treatment is investigational is that we do not know the likelihood of benefit that the patient will receive. It is possible that they will have great benefit, like some of the patients who have been transplanted from a brother or sister. It is possible that the side-effects of treatment may be too severe so that the transplant won't work.