More effective therapies are urgently needed against hepatitis C virus (HCV), a major cause of viral hepatitis. We used in vitro protein expression and microfluidic affinity analysis to study RNA binding by the HCV transmembrane protein NS4B, which plays an essential role in HCV RNA replication. We show that HCV NS4B binds RNA and that this binding is specific for the 3' terminus of the negative strand of the viral genome with a dissociation constant (Kd) of approximately 3.4 nM. A high-throughput microfluidic screen of a compound library identified 18 compounds that substantially inhibited binding of RNA by NS4B. One of these compounds, clemizole hydrochloride, was found to inhibit HCV RNA replication in cell culture that was mediated by its suppression of NS4B's RNA binding, with little toxicity for the host cell. These results yield new insight into the HCV life cycle and provide a candidate compound for pharmaceutical development.