This study will determine the safety and side effects of two experimental HIV vaccines and see if vaccination can enhance the pre-existing HIV-specific immune response in HIV-infected individuals on anti-retroviral therapy . The vaccines are VRC-HIVDNA016-00-VP (called the "DNA vaccine") and VRC-HIVADV014-00-VP (called the "rAd vaccine"). The DNA vaccine codes for four HIV proteins. The rAd vaccine is made using an adenovirus (a common virus that causes upper respiratory infections, such as the common cold) that has been modified to contain DNA that codes for three HIV proteins. These vaccines will be given in a "prime-boost" schedule and cannot cause HIV or adenoviral infections.