The study is done in 2 stages. In Stage 1, patients are randomized to receive placebo or 1 of 2 doses of AZT. Stage 1 lasts for 4 months. In Stage 2, patients who were initially treated with placebo are randomized again and all patients receive AZT. Stage 2 lasts an additional 12 months, during which time there are periodic medical and neurologic evaluations. Before beginning treatment, all patients have a lumbar puncture and a computerized tomographic (CT) scan of the brain. The lumbar puncture is repeated twice during and once at the end of Stage 1; the CT scan is also repeated at the end of Stage 1. Patients receiving AZT in either stage 1 or Stage 2 are seen by their physicians every week for the first 4 weeks and every other week thereafter for the first 4 months of receiving the drug. After 4 months, patients are seen by their physicians at 4 to 12 week intervals.