Patients are randomized to 1 of 3 groups for 12 months of treatment. Group 1 receives MK-639 plus AZT. Group 2 receives MK-639 alone. Group 3 receives AZT alone. Safety and tolerability are assessed by the incidence of clinical and laboratory adverse experiences. Blood and urine samples are collected for safety assessment and to determine CD4 cell counts and serum viral RNA levels. If therapy with MK-639 alone or with AZT is found to be generally safe and clinically efficacious, patients who have completed the study will have the opportunity to continue in an extension study protocol on a treatment regimen including MK-639.