Significance RNA viruses usurp and reprogram host cells using short RNA genomes. RNA viruses encode the information required for their replication in both their primary sequences and higher-order structures formed when the RNA genome strand folds back on itself, but the extent of higher-order structure has remained unclear. We use a new high-throughput RNA structure probing technology to identify RNA regions with tertiary folds and discover that roughly one-third of the dengue virus RNA genome forms higher-order interactions, many in regions functionally important for replication. This work suggests that tertiary structure elements might be common in large RNAs, and that these regions might contain pockets targetable by small molecules in the design of antiviral therapeutics.