Chronic Granulomatous Disease (CGD) is an inherited immunodeficiency disorder which results from defects that prevent white blood cells from effectively killing bacteria, fungi and other microorganisms. Chronic granulomatous inflammation may compromise vital organs and account for additional morbidity. CGD is thought to affect approximately 1 in 200,000 persons, although the real incidence might be higher due to under-diagnosis of milder phenotypes. The first gene therapy approaches in X-CGD have shown that effective gene therapy requires bone-marrow (BM) conditioning with chemotherapy to make space for the gene-modified cells to engraft. These studies demonstrated that transplantation of gene modified stem cells led to production of white blood cells that could clear existing infections. However, some trials using mouse-derived retroviral vectors were complicated by the development of myelodysplasia and leukemia-like growth of blood cells. This trial will evaluate a new lentiviral vector that may be able to correct the defect, but have much lower risk for the complication. This study is a two-part, prospective non-controlled, non-randomized Phase I/II clinical trial to assess the safety, feasibility and efficacy of cellular gene therapy in patients with chronic granulomatous disease using transplantation of autologous bone marrow CD34+ cells transduced ex vivo by the G1XCGD lentiviral vector containing the human CGD gene. Primary objectives include evaluation of safety and evaluation of efficacy by biochemical and functional reconstitution in progeny of engrafted cells and stability at 12 months. Secondary objectives include evaluation of clinical efficacy, longitudinal evaluation of clinical effect in terms of augmented immunity against bacterial and fungal infection, transduction of CD34+ hematopoietic cells from X-CGD patients by ex vivo lentivirus-mediated gene transfer, and evaluation of engraftment kinetics and stability. Approximately 3-6 patients will be treated per site with a goal of 16 total patients to be treated with G1XCGD lentiviral vector.