Patients in this study will continue to take their current (failing) antiretroviral regimen until they are registered to the study. Patients will be randomized to receive DAPD or placebo. Patients will receive DAPD or placebo together with ENF plus an OB regimen containing at least three but not more than five antiretroviral agents. The OB regimen will be selected based on the results of a screening HIV-1 drug resistance test and is expected to remain stable for at least the first 24 weeks of the study. Only ENF and DAPD will be supplied by this study, but they will not be provided to participants beyond the end of the study.