 Part B will last 15 months. In Part B, 72 participants will be randomly assigned to 1 of 2 groups. All Part B participants will receive 5 vaccinations. Group 5 will receive 5 vaccinations of either the HIV-1 gag vaccine plus IL-15 DNA or placebo; the vaccinations will occur at Months 0, 1, 3, 6, and 9. Group 7 will receive 3 vaccinations of the HIV-1 gag vaccine with a high dose of IL-15 adjuvant maximum tolerated dose from Part A followed by 2 vaccinations of the gag DNA vaccine with IL-12 DNA adjuvant. Some participants will receive placebo instead of this vaccine regimen. For Group 7, the HIV-1 gag vaccine with IL-15 adjuvant vaccinations will be given at Months 0, 1, and 3, and booster vaccinations will be given at Months 6 and 9. There will be 13 study visits in Part B. A physical exam, pregnancy prevention counseling, medication history, and adverse event reporting will occur at most visits. Urine and blood collection will occur at some visits. Participants will also be asked to complete questionnaires at certain visits. 