This study will last 40 to 104 weeks. IL-2 is provided as part of this study; potent ART is not provided. Patients in this study will receive potent ART with at least two scheduled potent ART interruptions. Patients will be randomly assigned to one of two treatment arms. Arm A patients will receive low-dose injections of IL-2 for 3 weeks, during the last 2 weeks of potent ART interruption periods and the first week of restarting potent ART. Arm B patients will receive high-dose injections of IL-2 during the first 5 days of restarting potent ART after the interruption period. The first two ART interruptions are 4 weeks in duration, followed by 12 weeks back on ART. Depending on the patient's viral load and CD4 count at Week 32, patients will either enter a third potent ART interruption for 12 to 48 weeks or will continue ART. No IL-2 will be given with the third scheduled potent ART interruption. Throughout the study, participants will have physical exams and laboratory tests, including measurements of viral load and CD4 count.