Part I: Patients add a 5-day course of subcutaneous IL-2 every 8 weeks for up to 48 weeks (6 cycles) to their HAART therapy. Three dose levels of IL-2 are administered. [AS PER AMENDMENT 5/3/01: It is strongly recommended, but not required, that] the first and second cycles of IL-2 are given in the hospital on an inpatient basis. The parent or patient is trained to give the injections and has the option of administering subsequent injections at home. Patients are monitored for CD4 and CD8 cell count and viral load. Enrollment into Part 1 begins at the lowest dose level; assuming no serious toxicities (Grade 3 or higher) occur, patients are enrolled into higher dose levels. The highest tolerated dose is established.