This is a clinical trial of gene therapy for X-linked severe combined immunodeficiency (XSCID), a genetic disease caused by defects in a protein called the common gamma chain, which is normally on the surface of immune cells called lymphocytes. XSCID patients cannot make T lymphocytes, and their B lymphocytes fail to make essential antibodies for fighting infections. Without T and B lymphocytes patients develop fatal infections in infancy unless they are rescued by a bone marrow transplant from a healthy donor. However, even transplanted patients may achieve only partial immune recovery and still suffer from many infections, auto-immunity and/or and poor growth. A recent, successful trial in France used gene therapy instead of bone marrow transplantation for infants with XSCID. This experience indicates that gene therapy can provide clinical benefit to XSCID patients. We will enroll eight older XSCID patients (1.5-20 years-old), who have previously received at least one bone marrow transplant, but still have poor T and B lymphocyte function that compromises their quality of life. Before enrollment, these subjects will have had some of their own blood-forming stem cells harvested and frozen in a blood bank. These cells have a defective gene, but a correct copy of the gene will be inserted while the cells are grown in sterile conditions outside the patient's body. To do this, the cells will be unfrozen and exposed for four days in a row to growth factors and particles of a retrovirus we have constructed and tested called "GALV MFGS-gc." Retrovirus particles will attach to the patient cells and introduce a correct copy of the common gamma chain gene into cells capable of growing into all types of blood cells, including T and B lymphocytes. XSCID patients who are enrolled in the study will receive a single dose of their own cells that have been modified by the GALV MFGS-gc treatment and also will be given another drug called palifermin to help prevent side effects from the chemotherapy and possibly try to improve the development of the T cells. After this, the patients will be monitored to find out if the treatment is safe and to see if their immune function improves. Study endpoints are (1) efficient and safe clinical-scale transduction of HSC from post-BMT XSCID subjects; (2) administration of a nonmyeloablative conditioning regimen in older patients to improve engraftment; (3) administration of a transduced HSC to eight subjects; (4) administration of KGF to improve thymic function post transplant to improve T cell development; and (5) appropriate follow-up of the treated subjects to monitor vector sequence distribution, gc expression in hematopoietic lineages, and lymphoctye numbers and function as well as general health and immune status.