It remains largely mysterious how the genomes of non-enveloped eukaryotic viruses are transferred across a membrane into the host cell. Picornaviruses are simple models for such viruses, and initiate this uncoating process through particle expansion, which reveals channels through which internal capsid proteins and the viral genome presumably exit the particle, although this has not been clearly seen until now. Here we present the atomic structure of an uncoating intermediate for the major human picornavirus pathogen CAV16, which reveals VP1 partly extruded from the capsid, poised to embed in the host membrane. Together with previous low-resolution results, we are able to propose a detailed hypothesis for the ordered egress of the internal proteins, using two distinct sets of channels through the capsid, and suggest a structural link to the condensed RNA within the particle, which may be involved in triggering RNA release.