The HIV-1 Tat protein interacts with TAR RNA and recruits CDK9/cyclin T1 and other host factors to induce HIV-1 transcription. Thus, Tat–TAR RNA interaction, which is unique for HIV-1, represents an attractive target for anti-HIV-1 therapeutics. To target Tat–TAR RNA interaction, we used a crystal structure of acetylpromazine bound to the bulge of TAR RNA, to dock compounds from the Enamine database containing over two million individual compounds. The docking procedure identified 173 compounds that were further analyzed for the inhibition of HIV-1 infection. The top ten inhibitory compounds with IC50 ≤ 6 µM were selected and the three least toxic compounds, T6780107 (IC50 = 2.97 μM), T0516-4834 (IC50 = 0.2 μM) and T5628834 (IC50 = 3.46 μM), were further tested for HIV-1 transcription inhibition. Only the T0516-4834 compound showed selective inhibition of Tat-induced HIV-1 transcription, whereas the T6780107 compound inhibited equally basal and Tat-induced transcription and the T5628834 compound only inhibited basal HIV-1 transcription. The compounds were tested for the inhibition of translation and showed minimal (<25%) effect. The T0516-4834 compound also showed the strongest inhibition of HIV-1 RNA expression and p24 production in CEM T cells and peripheral blood mononuclear cells infected with HIV-1 IIIB. Of the three compounds, only the T0516-4834 compound significantly disrupted Tat–TAR RNA interaction. Additionally, of the three tested compounds, T5628834 and, to a lesser extent, T0516-4834 disrupted Tat–CDK9/cyclin T1 interaction. None of the three compounds showed significant inhibition of the cellular CDK9 and cyclin T1 levels. In silico modelling showed that the T0516-4834 compound interacted with TAR RNA by binding to the bulge formed by U23, U25, C39, G26,C39 and U40 residues. Taken together, our study identified a novel benzoxazole compound that disrupted Tat–TAR RNA interaction and inhibited Tat-induced transcription and HIV-1 infection, suggesting that this compound might serve as a new lead for anti-HIV-1 therapeutics.