Dengue virus (DENV) and West Nile virus (WNV) are members of the Flavivirus genus of positive-strand RNA viruses. RNA sequences and structures, primarily in the untranslated regions, have been shown to modulate flaviviral gene expression and genome replication. Previously, we demonstrated that a structure in the DENV coding region (cHP) enhances translation start codon selection and is required for viral replication. Here we further characterize the role of the cHP in the DENV life cycle. We demonstrate that the cHP is required for efficient viral RNA synthesis in a sequence-independent manner. Viruses with a disrupted cHP are rescued by a spontaneous compensatory mutation that restabilizes the structure. Furthermore, the cHP, which is predicted to be conserved among arthropod-borne flaviviruses, is required for WNV replication. We propose that the cHP is a multifunctional determinant of flavivirus replication, functioning in both translation and RNA synthesis.