To compare the effect of zidovudine (AZT) given alone with the combination of AZT and acyclovir (ACV) on the human immunodeficiency virus (HIV) in persons infected with HIV, and to study the pharmacokinetics (how fast AZT reaches certain levels in blood and how long it remains), safety, and effectiveness of AZT given alone and in combination with ACV in treating HIV-infected patients. Other studies have shown that AZT offers potential benefits to specific AIDS patients when given over long time periods, and experiments in vitro (in the test tube) suggest that ACV may stimulate the action of AZT against HIV. It is necessary to obtain information on how these drugs perform in HIV-infected humans.