Latent HIV reservoirs are the primary hurdle to eradication of infection. Identification of agents, pathways and molecular mechanisms that activate latent provirus may, in the presence of highly active antiretroviral therapy, permit clearance of infected cells by the immune system. Promoter-proximal pausing of RNA polymerase (Pol) II is a major rate-limiting step in HIV gene expression. The viral Tat protein recruits human Super Elongation Complex (SEC) to paused Pol II to overcome this limitation. Here, we identify the bromodomain protein Brd4 and its inhibition of Tat-transactivation as a major impediment to latency reactivation. Brd4 competitively blocks the Tat–SEC interaction on HIV promoter. The BET bromodomain inhibitor JQ1 dissociates Brd4 from the HIV promoter to allow Tat recruitment of SEC to stimulate HIV elongation. JQ1 synergizes with another latency activator prostratin, which promotes Pol II loading onto the viral promoter. Because JQ1 activates viral latency without inducing global T cell activation, this and other closely related compounds and their antagonization of Brd4 to promote Tat–SEC interaction merit further investigations as effective agents/strategies for eliminating latent HIV.