Arthropod-borne RNA viruses pose a threat to human health throughout the world, but few treatments are available. A better understanding of the interactions between viruses and host cells will enable the development of new ways to combat these infections. During entry and replication, viral RNAs are exposed to host RNA-binding proteins with diverse functions. Some of these interactions have been studied, but many remain undefined. To understand how host RNA-binding proteins contribute to cellular defenses, we sought to characterize the antiviral functions of conserved DEAD-box helicase proteins identified by targeted screening in insect and mammalian host cells. Focusing on alphavirus and flavivirus infection, we assessed the effect of siRNA silencing of DDX23, DDX24, and DDX56 on infection by a panel of RNA viruses, and used CLIP-Seq to assess binding interactions of DDX56 on CHIKV and DENV RNAs during infection of human cells. We found a specific enrichment of DDX56 binding within the CHIKV nsP4 gene encoding the viral RNA-dependent RNA polymerase, which led us to investigate the role of DDX56 on initial steps of viral RNA translation and replication as an entering CHIKV genome launches replication within a host cell. We found that depletion of DDX56 improves stability of CHIKV genomes and increases levels of viral proteins, suggesting that DDX56 is capable of exerting an antiviral effect at the earliest stages of infection. The region of the CHIKV nsP4 gene bound by DDX56 is adjacent to a known structural element, and RNA folding algorithms predict structure in the DDX56 binding region as well. Taken together, these results suggest that DDX56 control of alphavirus infection likely involves recognition of a structural element that results in the CHIKV genome being targeted for degradation rather than launching replication. In contrast, CLIP-Seq analysis of DDX56 interactions with DENV RNA revealed lower and more uniform binding along the length of the viral genome, suggesting a less specific interaction and possibly a distinct antiviral mechanism. Together, these studies highlight the sensitivity of viral RNA to cellular factors shortly after entry and uncover additional virus-host interactions contributing to the control of infection.