 This study will last 18 months. CD8 cells will be isolated from the blood of HIV infected patients; the cells will be allowed to multiply in the laboratory, and patients will receive back their CD8 cells. Patients will receive up to 3 infusions of self CD8 cells. On Day 0, patients will receive their first infusion of CD8 cells. On Day 7, patients will receive their second infusion of CD8 cells; this infusion will be followed by 14 days of aldesleukin administered daily by injection under the skin. Patients with less than a Grade 2 toxicity will receive a third infusion of CD8 cells; this infusion will be followed by 21 days of aldesleukin. 