This study will investigate low-level viral loads in HIV-infected patients taking highly active antiretroviral therapy (HAART). Although HAART reduces viral levels and restores immune function to some degree, it does not cure HIV infection. The virus persists even at levels below that which it can be detected. This study will examine where this residual virus comes from in order to better understand the infection and the effectiveness of therapies. In addition, the study will 1) evaluate the ability of a new test to detect the virus at low levels; and 2) determine whether adding the protease inhibitor Kaletra to the HAART treatment regimen for patients with a low viral load will further decrease their viral load.