Current approaches used to identify protein-binding small molecules are not suited for identifying small molecules that can bind emerging RNA drug targets. By docking small molecules onto an RNA dynamic ensemble constructed by combining NMR spectroscopy and computational molecular dynamics, we virtually screened small molecules that target the entire structure landscape of the transactivation response element (TAR) from HIV type 1 (HIV-1). We quantitatively predict binding energies for small molecules that bind different RNA conformations and report the de novo discovery of six compounds that bind TAR with high affinity and inhibit its interaction with a Tat peptide in vitro (K_i values of 710 nM–169 μM). One compound binds HIV-1 TAR with marked selectivity and inhibits Tat-mediated activation of the HIV-1 long terminal repeat by 81% in T-cell lines and HIV replication in an HIV-1 indicator cell line (IC₅₀ ∼23.1 μM).