Respiratory syncytial virus (RSV) is a major cause of respiratory illness in young children, leading to significant morbidity and mortality worldwide. Despite its medical importance, no vaccine or effective therapeutic interventions are currently available. Therefore, there is a pressing need to identify novel antiviral drugs to combat RSV infections. Hsp90, a cellular protein-folding factor, has been shown to play an important role in the replication of numerous viruses. We here demonstrate that RSV requires Hsp90 for replication. Mechanistic studies reveal that inhibition of Hsp90 during RSV infection leads to the degradation of a viral protein similar in size to the RSV L protein, the viral RNA-dependent RNA polymerase, implicating it as an Hsp90 client protein. Accordingly, Hsp90 inhibitors exhibit antiviral activity against laboratory and clinical isolates of RSV in both immortalized as well as primary differentiated airway epithelial cells. Interestingly, we find a high barrier to the emergence of drug resistance to Hsp90 inhibitors, as extensive growth of RSV under conditions of Hsp90 inhibition did not yield mutants with reduced sensitivity to these drugs. Our results suggest that Hsp90 inhibitors may present attractive antiviral therapeutics for treatment of RSV infections and highlight the potential of chaperone inhibitors as antivirals exhibiting high barriers to development of drug resistance.