Part 1A: Twenty p24+ patients with AIDS or advanced ARC are randomized to 4 dosing groups of 5 patients each. Patients are treated with AZT for 6 weeks at ranging doses to determine a minimally effective dose (MED). At the end of week 6, each patient is sequentially assigned to 1 of 5 groups of rCD4 / AZT combination treatment. The first 3 patients to complete treatment through week 6 are treated in group A, the next 3 patients in group B, and so on. The treatment period is 4 weeks. Each patient continues on his or her AZT dose as initially administered. The highest dose of AZT that produces less than a 50 percent drop in HIV-1 p24 antigen levels in at least 3 of 5 patients over 6 weeks will be the MED of AZT and will be known as the AZT MED. After the MED is determined, Part 1B begins. Part 1B: 20 patients are randomized to 2 different dosing groups: Group 5: AZT MED (weeks 1 to 8), then AZT MED plus rCD4 (weeks 9 to 16); Group 6: AZT MED plus rCD4 (weeks 1 to 8), then AZT MED (weeks 9 to 16). Part 2: Part 2 begins once accrual to Part 1B is completed. If fewer than 10 of 20 patients exhibit a drop of at least 50 percent in p24 antigen level after receiving AZT and rsCD4 combination treatment, entry to Part 2 will be interrupted and the study design will be reevaluated. In Part 2, 10 patients are randomly assigned to one of four groups. Patients within each group receive two 8 week treatment courses. These two treatment courses are 8 weeks with the AZT MED alone, and 8 weeks of treatment with the combination of the AZT MED plus rCD4.