Studies have shown that inactivated, gp120-depleted whole virus immunogen (Remune) boosts immune responses to HIV. One response, lymphocyte proliferative response (LPR) to p24, is correlated with a low viral load in some patients with long-term non-progression of disease. This study examines whether administering Remune vaccine may generate new immune responses or boost existing responses to keep the level of virus in the blood low for a longer period of time than antiretroviral therapy alone. [AS PER AMENDMENT 7/20/00: In a recent study using Remune, comparison of virologic failure and time to virologic failure between Remune and adjuvant placebo arms revealed no differences between the 2 arms of the study. Results of this study suggest that the hypothesis in A5057 (that recipients of Remune would have only 50 percent of the number of virologic relapses as occur in the control arm) is no longer plausible in its current design. This protocol is being redesigned.] A substudy adds the HIV canarypox vaccine (vCP1452) in patients in the parent study and evaluates whether canarypox vaccine can augment the immune responses of Remune.