This is a non-randomized clinical trial using a lentiviral gene transfer vector (or lentivector, LV) to treat patients with X-linked severe combined immunodeficiency (XSCID) who have clinically significant impairment of immunity. We will collect the patient s own stem cells that will be transduced or exposed to the vector carrying a normal copy of the gene. The gene-corrected stem cells will be administered as a one-time infusion. Patients will receive a low-moderate dose of a chemotherapy drug called busulfan (6 mg/kilogram body weight) to allow engraftment of the stem cells. After the infusion, patients will be monitored to see if the treatment is safe and whether their immune system improves. Patients will be monitored for up to 15 years after treatment to assess immune function and the safety of the treatment. XSCID is a genetic disease caused by defects in the common gamma chain, a protein found at the surface of immune cells called lymphocytes, and is necessary to their growth and function. XSCID patients cannot make T-lymphocytes necessary to fight infections, and their B-cells fail to make essential antibodies. Without normal T-and B-lymphocyte function, patients develop fatal infections in infancy unless they receive a bone marrow transplant from a healthy donor. The best type of transplant is from a tissue-matched healthy sibling, but most XSCID patients do not have a tissue-matched sibling and are treated with a transplant from a parent who is only half-matched by tissue typing. While a half-matched transplant from a parent can be lifesaving for an infant with XSCID, a subset of patients fail to achieve sufficient long-lasting restoration of immunity to prevent infections and other chronic problems. Trials of gene transfer treatments using mouse retrovirus vectors for infants with XSCID have been performed and have shown this type of gene transfer can be an alternate approach for significantly restoring immunity to infants with XSCID. However, among the 18 infants with XSCID benefiting long-term from the gene transfer treatment, 5 developed T-lymphocyte leukemia and 1 died of this leukemia. When older children with XSCID were treated with gene transfer, the restoration of immunity was much less than seen in the infants. These observations of gene transfer treatments using mouse retrovirus vectors to treat infants and older patients with XSCID suggest that safer and more effective vectors were needed and that there also may be a need to give chemotherapy or another mode of conditioning to increase engraftment in the marrow of the gene-corrected blood stem cells. Our data and other published studies suggest that lentivectors derived from the human immunodeficiency virus and have the properties of our highly modified vector have a reduced interaction with nearby genes and therefore less of a tendency to activate genes that may lead to cancer formation. This type of lentivector may work better at getting into blood stem cells. The study's purpose is to evaluate the safety and effectiveness of lentiviral gene transfer treatment in restoring immune function to 35 XSCID patients who are 2 to 40 years of age and have significant impairment of immunity. Early evidence for effectiveness will be defined by appearance and expansion in the circulation of the patient s gene-corrected T-lymphocytes with a functional \>=c gene and improved laboratory measures of immune function. The primary endpoint for efficacy will be at 2 years after treatment and will include these laboratory parameters plus evidence for clinical benefit. Evidence for safety will focus on the maintenance of a diversity of gene-marked cells and no occurrence of abnormal patterns of production of blood cells or any leukemia or other cancer.