PEG-Intron is an experimental drug that works differently than other anti-HIV medications. It decreases the ability of HIV to infect the T cells (a special type of cell that helps fight infection). PEG-Intron has been approved by the Food and Drug Administration (FDA) to treat hepatitis C in adults, but in this study, it is being used as an investigational agent for the treatment of HIV/AIDS. It has not been tested in children before and experience with PEG-Intron in adults is limited. (This protocol has been changed to reflect FDA approval of PEG-Intron for treating hepatitic C in adults.)