Thirty-six children who are varicella zoster virus (VZV)-naive (treatment group) receive Varivax at Weeks 0 and 12, with a possible boost at Week 52 if the patient is still seronegative for VZV and cytomegalovirus infection. Twenty children who have a history of wild-type varicella exposure within the past year (control group) receive no study treatment. All patients are either asymptomatic or mildly symptomatic for HIV infection. Patients make 12-14 visits to the clinic. [AS PER AMENDMENT 9/9/99: This study has been reorganized into two cohorts (asymptomatic and symptomatic). In the asymptomatic cohort, accrual has been completed with 40 patients in Treatment Group I and 19 in the control group. This phase of the study demonstrated that Varivax was well tolerated in 48 HIV-infected children with asymptomatic disease. The symptomatic cohort includes Treatment Groups II and III, each with 30 patients. The first 10 patients from Group II are monitored for 42 days following the first dose of vaccine before the remaining 20 are accrued. Once the first 10 patients in Group II have been evaluated with acceptable toxicity and immunologic profiles, the remaining 20 Group II and the first 10 Group III patients are enrolled. The first 10 Group III patients are also followed for acceptable toxicity and immunologic response before accrual of the remaining 20 Group III patients.]