Two immunologic cohorts are enrolled. Cohort A includes children with a CD4 cell percentage greater than or equal to 20 percent that has been documented as stable for at least the 6 months prior to the time varicella developed (confirmed by a minimum of 2 tests) and a CD4 cell percentage greater than [AS PER AMENDMENT 10/27/99: or equal to] 15 percent that has been documented as stable for at least the 6 months prior to enrollment (confirmed by a minimum of 2 tests). Cohort B includes children with a CD4 cell percentage greater than or equal to 10 percent and less than 15 percent that has been documented as stable for at least the 6 months prior to the time varicella developed and stable for at least the 6 months prior to enrollment (confirmed by a minimum of 2 tests). [AS PER AMENDMENT 4/20/01: Cohort B includes children who have a CD4 cell percentage less than 15% documented by a minimum of 1 but preferably 2 tests within 1 year of onset of varicella (i.e., within 1 year before to 1 year after varicella) and a CD4 cell percentage greater than or equal to 15% documented by a minimum of 2 tests at the time of enrollment.] A pilot study precedes the full study. [AS PER AMENDMENT 10/27/99: The pilot study for Cohort A precedes the full study for Cohort A and the pilot study for Cohort B. The pilot study for Cohort B precedes the full study for Cohort B.] The pilot study includes 10 children from each cohort who receive live-attenuated VZV at Weeks 0 and 8. If 3 pilot-study patients in a cohort meet a toxicity endpoint related to the vaccine, the dose regimen has failed the safety criteria for that cohort. [AS PER AMENDMENT 10/27/99: If 3 children in the pilot study for Cohort A meet a toxicity endpoint deemed to be related to the vaccine, the dose regimen has failed safety criteria for both cohorts. If 3 children in the pilot phase of Cohort B meet a toxicity endpoint deemed related to the vaccine, the dose regimen has failed the safety criteria for Cohort B.] If, at 12 weeks after immunization, at least 5 pilot-study patients in a cohort respond and the safety profile is deemed adequate, the pilot study extends into a full study with the immunization of an additional 20 patients from that cohort. [AS PER AMENDMENT 10/27/99: If, at Week 12, at least 5 pilot-study patients in Cohort A meet immunologic criteria and the safety profile is deemed adequate, then the full study for Cohort A and the pilot study for Cohort B opens. If the same immunologic and safety criteria are met for the pilot study for Cohort B, then the full study for Cohort B opens.] If either cohort shows an inadequate immunologic response or safety profile, the study team reviews the results to determine if another regimen should be considered. In the full study, patients receive 2 immunizations, at Weeks 0 and 8. Varicella antibody titers and in vitro responder cell frequency (RCF) assays are measured at Weeks 0, 4, 8, 12, 24, 52, 78, and 104. Symptoms, HIV progression, and VZV presence are monitored throughout the study.