Evaluating the Safety and Immune Response to an HIV Vaccine in Healthy, HIV-Uninfected Adults Who Have Participated in Previous HIV Vaccine Clinical Trials and in Adults Who Have Not Participated in Previous HIV Vaccine Clinical Trials

Inclusion Criteria: * Access to a participating HVTN Clinical Research Site (CRS) and willing to be followed for the planned duration of the study * Able and willing to provide informed consent * Assessment of understanding: must demonstrate understanding of this study and the Step Study results; completes a questionnaire prior to first vaccination with verbal demonstration of understanding of all questionnaire items answered incorrectly * Willing to receive HIV test results * Willing to discuss HIV infection risks, amenable to HIV risk reduction counseling, and committed to maintaining behavior consistent with low risk of HIV exposure through the last required study clinic visit * Assessed by the clinic staff as being at low risk for HIV infection * Agrees not to enroll in another study of an investigational research agent prior to completion of last required study clinic visit * In good general health as shown by medical history, physical exam, and screening laboratory tests * For Group 1: Prior receipt of an HIV-1 subtype B envelope subunit vaccine (gp120, gp140) with MF59 adjuvant. More information on this criterion can be found in the protocol. * Hemoglobin greater than or equal to 11.0 g/dL for participants who were born female, greater than or equal to 13.0 g/dL for participants who were born male * White blood cell (WBC) count equal to 3,300 to 12,000 cells/mm\^3 * Total lymphocyte count greater than or equal to 800 cells/mm\^3 * Remaining differential either within …