 The function of CD8 cells in the human body is to kill infected target cells, such as HIV infected cells. Recent data suggest that intravenous administration of HIV-specific CD8 cells is safe, augments host immunity, and mediates a dramatic reduction in circulating HIV-infected CD4 cells. However, the observed antiviral effects are transient, and HIV infected CD4 cells re-emerge as the number of self CD8 cells declines. Augmenting CD8 cell response to HIV by immunotherapy with CD8 cells may be a useful addition to drug therapy if the infused CD8 cells can survive long-term in vivo. Administration of interleukin-2 also known as aldesleukin or IL-2, a naturally occurring cytokine, has been proposed as a way to maintain the number of CD8 cells. This study will evaluate the safety and efficacy of immunotherapy with HIV-specific CD8 cells in HIV infected patients. Additionally, this study will determine if aldesleukin injections improve the persistence of self CD8 transplants and the duration of antiviral activity without severe toxicity. 