Participants are randomized to 1 of 2 groups. People in Group A receive either 2 injections of a lower dose (300 mcg) of the DNA plasmid vaccine or the placebo control. People in Group B receive either 2 injections of a higher dose (3000 mcg) of the DNA plasmid vaccine or the control. Group B will be enrolled only if the vaccine is found to be safe and well-tolerated during the initial 2-week evaluation of all participants in Group A. Participants receive vaccinations administered at Months 0 and 2. All vaccinations are administered by intramuscular (IM) injection in an outpatient setting. Participants have about 10 clinic visits during this study, including the screening and injection visits. Participants give blood and urine samples at study visits. They are tested for HIV before entering the study and 4 more times during the study. Women who can become pregnant may undergo up to 3 pregnancy tests during the study period.