This is a phase I-II dose escalation study of clarithromycin in combination with zidovudine (AZT) in persons with HIV infection. Clarithromycin is an investigational macrolide antibiotic with in vitro activity against Mycobacterium avium-intracellulare (MAI) and Toxoplasma gondii. This activity makes it an attractive agent for investigation in patients with HIV infection who are prone to opportunistic infections with these organisms. Although the drug has been tested in approximately 4000 persons, it has not been tested systematically in HIV infected persons, no maximally tolerated dose (MTD) has been determined, and its interaction with AZT is unknown. This study will evaluate the tolerance of clarithromycin with AZT and determine a MTD in combination with AZT. Additionally, for persons who are found to be bacteremic with MAI, extended courses of clarithromycin will be offered to determine the clinical and microbiological responses to clarithromycin.