Retroviruses selectively package two copies of their RNA genomes in the context of a large excess of nongenomic RNA. Specific packaging of genomic RNA is achieved, in part, by recognizing RNAs that form a poorly understood dimeric structure at their 5' ends. We identify, quantify the stability of, and use extensive experimental constraints to calculate a 3D model for a tertiary structure domain that mediates specific interactions between RNA genomes in a gamma retrovirus. In an initial interaction, two stem-loop structures from one RNA form highly stringent cross-strand loop-loop base pairs with the same structures on a second genomic RNA. Upon subsequent folding to the final dimer state, these intergenomic RNA interactions convert to a high affinity and compact tertiary structure, stabilized by interdigitated interactions between U-shaped RNA units. This retroviral conformational switch model illustrates how two-step formation of an RNA tertiary structure yields a stringent molecular recognition event at early assembly steps that can be converted to the stable RNA architecture likely packaged into nascent virions.