Narnaviruses are RNA viruses detected in diverse fungi, plants, protists, arthropods, and nematodes. Though initially described as simple single-gene nonsegmented viruses encoding RNA-dependent RNA polymerase (RdRp), a subset of narnaviruses referred to as "ambigrammatic" harbor a unique genomic configuration consisting of overlapping open reading frames (ORFs) encoded on opposite strands. Phylogenetic analysis supports selection to maintain this unusual genome organization, but functional investigations are lacking. Here, we establish the mosquito-infecting Culex narnavirus 1 (CxNV1) as a model to investigate the functional role of overlapping ORFs in narnavirus replication. In CxNV1, a reverse ORF without homology to known proteins covers nearly the entire 3.2-kb segment encoding the RdRp. Additionally, two opposing and nearly completely overlapping novel ORFs are found on the second putative CxNV1 segment, the 0.8-kb "Robin" RNA. We developed a system to launch CxNV1 in a naive mosquito cell line and then showed that functional RdRp is required for persistence of both segments, and an intact reverse ORF is required on the RdRp segment for persistence. Mass spectrometry of persistently CxNV1-infected cells provided evidence for translation of this reverse ORF. Finally, ribosome profiling yielded a striking pattern of footprints for all four CxNV1 RNA strands that was distinct from actively translating ribosomes on host mRNA or coinfecting RNA viruses. Taken together, these data raise the possibility that the process of translation itself is important for persistence of ambigrammatic narnaviruses, potentially by protecting viral RNA with ribosomes, thus suggesting a heretofore undescribed viral tactic for replication and transmission. IMPORTANCE Fundamental to our understanding of RNA viruses is a description of which strand(s) of RNA are transmitted as the viral genome relative to which encode the viral proteins. Ambigrammatic narnaviruses break the mold. These viruses, found broadly in fungi, plants, and insects, have the unique feature of two overlapping genes encoded on opposite strands, comprising nearly the full length of the viral genome. Such extensive overlap is not seen in other RNA viruses and comes at the cost of reduced evolutionary flexibility in the sequence. The present study is motivated by investigating the benefits which balance that cost. We show for the first time a functional requirement for the ambigrammatic genome configuration in Culex narnavirus 1, which suggests a model for how translation of both strands might benefit this virus. Our work highlights a new blueprint for viral persistence, distinct from strategies defined by canonical definitions of the coding strand.