Participants are randomized to receive either oral AZT or HIVIG. Patients may receive treatment for a maximum of 48 weeks. Patients are evaluated during treatment at weeks 2, 4, and every 4 weeks thereafter. Infants who are receiving HIVIG initially are treated with the appropriate age-adjusted dose of oral AZT in addition to HIVIG if they meet clinical disease progression criteria. All participants who have completed 48 weeks of treatment or who are discontinued from treatment are followed every 3 months for an additional 48 weeks. This follow-up may be conducted over the telephone.