This study will last at least 3 years. Participants will be randomly assigned to one of two groups at study entry. Group A participants will receive 3TC/ZDV twice daily and EFV once daily at study enrollment. Participants receiving TB therapy at the time of enrollment may be observed for 2 weeks prior to beginning early therapy. Dosage adjustment of EFV may be necessary for participants receiving rifampin as part of their TB therapy. Group B participants will receive 3TC/ZDV twice daily and EFV once daily when they develop clinical AIDS or their CD4 count drops below 200 cells/mm3 (WHO Stage IV). Directly observed therapy will be used for the first two months of treatment for every participant.