This study will test the safety and effectiveness of hydroxyurea, an anti-cancer drug, given together with the anti-HIV drugs didanosine, stavudine and efavirenz for treating children infected with human immunodeficiency virus (HIV). Some studies have found that hydroxyurea may help certain anti-HIV drugs to work better and that the virus does not become resistant to it, as it does other drugs. This study will also examine how hydroxyurea affects the body's immune system and virus levels.