This study uses autologous (one's own) CD4 T cells modified with a viral vector expressing a genetic antisense targeting HIV, this vector is called VRX496. Study treatment is by intravenous infusion of vector modified cells and infusions will be provided every other week for a total of 4 or 8 doses. These modified cells, once infused, may provide immune support and are not destroyed by HIV, and thus may delay or reverse HIV disease progression. The study will enroll up to 40 male and female HIV-positive subjects in up to 8 centers. Subjects will be 18 years of age and over who have failed or are intolerant to at least one triple combination of antiretroviral drugs. Subjects must have a viral load between 5,000 and 200,000 copies/ml and a CD4+ count of ≥150, be in good health and have no evidence of active opportunistic infection, heart disease, or bleeding disorders. Subjects must not be on corticosteroids, immunomodulating agents or hydroxyurea. Subjects must not have received an AIDS vaccine or any investigational gene therapy product at any time. Females must not be pregnant or breastfeeding.