Despite antiretroviral therapy (ART), human immunodeficiency virus (HIV)-1 persists in a stable latent reservoir(1,2), primarily in resting memory CD4(+) T cells(3,4). This reservoir presents a major barrier to the cure of HIV-1 infection. To purge the reservoir, pharmacological reactivation of latent HIV-1 has been proposed(5) and tested both in vitro and in vivo(6-8). A key remaining question is whether virusspecific immune mechanisms, including cytotoxic T lymphocytes (CTLs), can clear infected cells in ART-treated patients after latency is reversed. Here we show that there is a striking all or none pattern for CTL escape mutations in HIV-1 Gag epitopes. Unless ART is started early, the vast majority (>98%) of latent viruses carry CTL escape mutations that render infected cells insensitive to CTLs directed at common epitopes. To solve this problem, we identified CTLs that could recognize epitopes from latent HIV-1 that were unmutated in every chronically infected patient tested. Upon stimulation, these CTLs eliminated target cells infected with autologous virus derived from the latent reservoir, both in vitro and in patient-derived humanized mice. The predominance of CTL-resistant viruses in the latent reservoir poses a major challenge to viral eradication. Our results demonstrate that chronically infected patients retain abroad-spectrum viral-specific CTL response and that appropriate boosting of this response may be required for the elimination of the latent reservoir.