In order for a virus to persist, there must be a balance between viral replication and immune clearance. It is commonly believed that adaptive immunity drives clearance of viral infections and, thus, dysfunction or viral evasion of adaptive immunity is required for a virus to persist. Type I interferons (IFNs) play pleiotropic roles in the antiviral response, including through innate control of viral replication. Murine norovirus (MNoV) replicates in dendritic cells (DCs) and type I IFN signaling in DCs is important for early control of MNoV replication. We show here that the non-persistent MNoV strain CW3 persists systemically when CD11c positive DCs are unable to respond to type I IFN. Persistence in this setting is associated with increased early viral titers, maintenance of DC numbers, increased expression of DC activation markers and an increase in CD8 T cell and antibody responses. Furthermore, CD8 T cell function is maintained during the persistent phase of infection and adaptive immune cells from persistently infected mice are functional when transferred to Rag1-/- recipients. Finally, increased early replication and persistence are also observed in mixed bone marrow chimeras where only half of the CD11c positive DCs are unable to respond to type I IFN. These findings demonstrate that increased early viral replication due to a cell-intrinsic innate immune deficiency is sufficient for persistence and a functional adaptive immune response is not sufficient for viral clearance.