The evolutionary history that led to Eocene-and-later primates of modern aspect (Euprimates) has been uncertain. We describe a skeleton of Paleocene plesiadapiform Carpolestes simpsoni that includes most of the skull and many postcranial bones. Phylogenetic analyses indicate that Carpolestidae are closely related to Euprimates. C. simpsoni had long fingers and an opposable hallux with a nail. It lacked orbital convergence and an ankle specialized for leaping. We infer that the ancestor of Euprimates was primitively an arboreal grasper adapted for terminal branch feeding rather than a specialized leaper or visually directed predator.