The purpose of this study is to see if adding an HIV vaccine (ALVAC-HIV vCP1452), IL-2 (interleukin-2, a protein found in the blood that helps boost the immune system), or both to anti-HIV-drug therapy is safe, tolerable, and effective in controlling viral load (level of HIV in the body). (This study has been changed to clarify drug name.) Anti-HIV drugs can help reduce a patient's viral load. However, HIV can still remain in CD4 cells (cells of the immune system that help fight infection). Combining an HIV vaccine, IL-2, or both with anti-HIV drugs may help reduce the number of HIV-infected cells.