Antiretroviral therapy can effectively suppress HIV-1 infection but is ineffective against integrated proviruses. A latent viral reservoir composed of latently infected CD4(+)T cells persists under suppressive therapy, and infected individuals must remain indefinitely on antiretroviral therapy to prevent viral reactivation and propagation. Despite therapy, some degree of low-level ongoing replication is detected and transient viral reactivation may replenish the latent reservoir. An analog of the natural compound, Cortistatin A, blocks HIV-1 transcription by specifically targeting the viral transactivator, Tat. Treatment of latently infected cells with this Tat inhibitor promotes a state of deep-latency from which HIV reactivation capacity is greatly diminished. Here we discuss the use of Tat inhibitors to limit the latent reservoir to achieve a functional cure.