To evaluate the clinical, immunologic, and virologic effects of oral zidovudine (AZT) plus intravenous immunoglobulin (IVIG) versus AZT plus placebo (albumin). It is estimated that by 1991, there may be 10,000 to 20,000 HIV-infected children in the United States. HIV infection in children is most often associated with symptomatic disease and poor prognosis. Treatment with antiviral therapy may be effective in changing the course of disease and decreasing mortality in this vulnerable population. AZT treatment has been shown to decrease mortality and the frequency of opportunistic infections in certain adult AIDS patients; therefore, it is likely that children may also benefit from this antiviral therapy. In addition, bacterial infections are frequently found in HIV-infected children. Because pooled human serum immunoglobulin, another name for antibodies, is effective in reducing bacterial infection in patients with defects of immunity, it may reduce the rate of bacterial infection in HIV-infected children as well. In this study, AZT will be administered together with IVIG to determine safety, tolerance, and efficacy of the combined treatment.