The rising threat of pandemic viruses, such as SARS-CoV-2, requires development of new preclinical discovery platforms that can more rapidly identify therapeutics that are active in vitro and also translate in vivo. Here we show that human organ-on-a-chip (Organ Chip) microfluidic culture devices lined by highly differentiated human primary lung airway epithelium and endothelium can be used to model virus entry, replication, strain-dependent virulence, host cytokine production, and recruitment of circulating immune cells in response to infection by respiratory viruses with great pandemic potential. We provide a first demonstration of drug repurposing by using oseltamivir in influenza A virus-infected organ chip cultures and show that co-administration of the approved anticoagulant drug, nafamostat, can double oseltamivir9s therapeutic time window. With the emergence of the COVID-19 pandemic, the Airway Chips were used to assess the inhibitory activities of approved drugs that showed inhibition in traditional cell culture assays only to find that most failed when tested in the Organ Chip platform. When administered in human Airway Chips under flow at a clinically relevant dose, one drug amodiaquine significantly inhibited infection by a pseudotyped SARS-CoV-2 virus. Proof of concept was provided by showing that amodiaquine and its active metabolite (desethylamodiaquine) also significantly reduce viral load in both direct infection and animal-to-animal transmission models of native SARS-CoV-2 infection in hamsters. These data highlight the value of Organ Chip technology as a more stringent and physiologically relevant platform for drug repurposing, and suggest that amodiaquine should be considered for future clinical testing.