Hepatitis C virus (HCV) infects over 170 million people worldwide and is a leading cause of liver disease and cancer. The virus has a 9,650-nt, single-stranded, messenger-sense RNA genome that is infectious as an independent entity. The RNA genome has evolved in response to complex selection pressures, including the need to maintain structures that facilitate replication and to avoid clearance by cell-intrinsic immune processes. Here we used high-throughput, single-nucleotide resolution information to generate and functionally test data-driven structural models for three diverse HCV RNA genomes. We identified, de novo, multiple regions of conserved RNA structure, including all previously characterized cis-acting regulatory elements and also multiple novel structures required for optimal viral fitness. Well-defined RNA structures in the central regions of HCV genomes appear to facilitate persistent infection by masking the genome from RNase L and double-stranded RNA-induced innate immune sensors. This work shows how structure-first comparative analysis of entire genomes of a pathogenic RNA virus enables comprehensive and concise identification of regulatory elements and emphasizes the extensive interrelationships among RNA genome structure, viral biology, and innate immune responses.