Evaluating the Safety and Immune Response of DNA/MVA Vaccines in HIV-1-Infected Young Adults Taking Anti-HIV Medications

Inclusion Criteria: * HIV-1 infected. More details on this criterion can be found in the protocol. * Likely HIV-1 acquisition in North America or Europe (in the opinion of the site investigator) * Likely HIV-1 acquisition from sexual transmission (in the opinion of the site investigator) * On stable HAART, defined as at least three different antiretrovirals (ARVs) from two different classes, with plasma HIV-1 RNA levels fewer than 100 copies/mL for at least 12 months prior to screening. Furthermore, at least two plasma HIV-1 RNA levels fewer than 100 copies/mL (and none with plasma HIV-1 RNA levels 100 or more copies/mL), separated by at least 3 months must have been documented during the 6-month period prior to enrollment. * Ability and willingness of participant to provide signed written informed consent * CD4 count 400 cells/mm\^3 or greater at screening * The following lab values (at screening visit): * Creatine phosphokinase no higher than 5 times the upper limit of normal (ULN). More details on this criterion can be found in the protocol. * Troponin I no more than 1.0 times ULN * Hemoglobin greater than 10 g/dL * Absolute neutrophil count greater than 1,000 mm\^3 * Platelets greater than 100,000 mm\^3 * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) no greater than 1.5 times ULN * Total bilirubin no greater than 1.5 times ULN (less than 5 times ULN if taking atazanavir) * Creatinine less than 2.0 mg/dL * Female participants who engage in sexual activity that could lead to pregnancy must agree to avoid pregnancy and to consistently use two methods of contraception, including at least one form of barrier contraception, from the screening visit until 90 days after the final vaccination. Medically acceptable contraceptives include barrier methods (such as a condom or diaphragm) used with a spermicide, an intrauterine device (IUD), or approved hormonal contraceptives, such as birth control pills, Depo Provera, or Lupron Depot. Condoms are recommended because their appropriate use is the only contraception method effective for preventing HIV-1 transmission. Two methods of barrier contraception (condom and diaphragm) may be combined to meet this requirement. Sexually active female study participants without reproductive potential are eligible without requiring the use of contraception. Written or oral documentation communicated by clinician or clinician's staff from one of the following is required for participants: physician report/letter or discharge summary. * To prevent pregnancies, male participants must agree to not attempt to impregnate a female or participate in sperm donation programs. Males engaging in sexual activity that could lead to pregnancy must use a condom from the date of receipt of the first study vaccine until 90 days after receipt of the last study vaccine. * To prevent HIV-1 transmission to a partner, all participants participating in sexual activity must agree to use effective barrier methods (condoms) * Willing to comply with all study requirements, including adherence to ARV treatment as prescribed by regular healthcare provider and the expectation to be available for the duration of the study Exclusion Criteria: * Documentation of infection with HIV-1 other than Clade B (e.g., if genotype data are available from pre-treatment viral resistance analyses) * Documentation that the last CD4 T-cell count prior to the initiation of ARV was fewer than 300 cells/mm\^3 * Hepatitis B surface antigen positive * Hepatitis C virus RNA positive * History of or known active cardiac disease including: * evidence of past or evolving myocardial infarction * angina pectoris * congestive heart failure with permanent sequelae * cardiomyopathy (hypertrophic or dilated) * myocarditis * pericarditis * clinically significant arrhythmia (including any arrhythmia requiring medication, treatment, or clinical follow-up) * stroke or transient ischemic attack * anginal chest pain or shortness of breath with mild activity (such as walking upstairs) due to cardiac disease (New York Heart Association \[NYHA\] class 2-4) * Screening ECG with clinically significant findings or features that would interfere with the assessment of myo/pericarditis, including any of the following: * Conduction disturbance (complete left or complete right bundle branch block or nonspecific intraventricular conduction disturbance with QRS greater than 120 ms, atrioventricular (AV) block of any degree, or QTc prolongation (greater than 450 ms) * Pathologic repolarization (ST segment or T wave) abnormality * Significant atrial or ventricular arrhythmia * Frequent atrial or ventricular ectopy (e.g., frequent premature atrial contractions, multifocal or two or more premature ventricular contractions in a row) * Clinically significant, HIV-related renal disease at screening or enrollment (creatinine at least 2.0 mg/dL; persistent high grade proteinuria greater than 2+). If either of these findings is present at screening, tests may be repeated once with option for enrollment if these findings resolve. * Past or present, HIV-related neurocognitive disease identified by a care provider * Known hypersensitivity to vaccine components * Receipt of chemotherapy for active malignancy in the past 12 months * Prior vaccinations with any HIV-1 vaccine * Prior immunization with any poxvirus, including vaccinia * Receipt of immunomodulatory agents, oral or injected systemic corticosteroids for more than 7 days at a time (including nonprescription street steroids), gamma globulin, or investigational agents within 6 months of screening. Use of intranasal or inhaled corticosteroids is allowed. * Receipt of any other live licensed vaccine within 4 weeks or inactivated licensed vaccine within 2 weeks prior to study enrollment * Pregnancy or breastfeeding * Current documented or suspected serious bacterial infection, metabolic illness, malignancy, or immediate life-threatening conditions * Any clinically significant diseases (other than HIV infection) or clinically significant findings during the screening medical history or physical examination that, in the site investigator's opinion, would compromise the outcome of this study * Active alcohol or substance abuse (abuse is defined as use of alcohol or other substance such that it is likely to interfere with the ability of the participant to adhere to medications or to return for study visits or is likely to lead to AEs) * Any foreseeable circumstances that, in the opinion of the site investigator, are likely to jeopardize participant adherence to HAART (i.e., insurance problems, housing instability, or unemployment)