This study is a 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 3-5 patients will be treated per site with a goal of 10 total patients to be treated with G1XCGD lentiviral vector.