HIV-infected patients usually are not offered bone marrow transplant treatments because they are at increased risk of dying from the intense chemotherapy and radiation therapy used for the procedure. This study uses a modified procedure, transplanting stem cells instead of bone marrow, designed to be less dangerous for such patients. Patients will also undergo a procedure called gene transfer to try to halt progression of their HIV infection. The procedure in this study differs from standard bone marrow transplantation in three ways: