Viruses are molecular machines sustained through a life cycle that requires replication within host cells. Throughout the infectious cycle, viral and cellular components interact to advance the multistep process required to produce progeny virions. Despite progress made in understanding the virus-host protein interactome, much remains to be discovered about the cellular factors that function during infection, especially those operating at terminal steps in replication. In an RNA interference screen, we identified the eukaryotic chaperonin T-complex protein-1 (TCP-1) ring complex (TRiC; also called CCT for chaperonin containing TCP-1) as a cellular factor required for late events in the replication of mammalian reovirus. We discovered that TRiC functions in reovirus replication through a mechanism that involves folding the viral sigma 3 major outer-capsid protein into a form capable of assembling onto virus particles. TRiC also complexes with homologous capsid proteins of closely related viruses. Our data define a critical function for TRiC in the viral assembly process and raise the possibility that this mechanism is conserved in related non-enveloped viruses. These results also provide insight into TRiC protein substrates and establish a rationale for the development of small-molecule inhibitors of TRiC as potential antiviral therapeutics.