This study will test the safety and effectiveness of genetically altered T lymphocytes (white blood cells of the immune system) in reducing viral load in patients infected with the human immunodeficiency virus (HIV). The lymphocytes will have two genes inserted into them; a laboratory-manufactured anti-HIV gene designed to inhibit HIV reproduction (either the RevTD or Rev-TD-antiTAR gene), and a "marker" gene that will show whether or not the inserted genes have gotten into the cells.