Bats are the only mammals capable of powered flight. One of the oldest bats known from a complete skeleton is Onychonycteris finneyi from the Early Eocene (Green River Formation, Wyoming, 52.5 mya). Estimated to weigh ~40 g, Onychonycteris exhibits the most primitive combination of characters thus far known for bats. Here we reconstructed the aerofoil of the two known specimens, calculated basic aerodynamic variables, and compared them with those of extant bats and gliding mammals. Onychonycteris appears in the edges of the morphospace for bats, underscoring the primitive conformation of its flight apparatus. Low aerodynamic efficiency is inferred for this extinct species as compared to any extant bat. When we estimated aerofoil variables in a model of Onychonycteris excluding the handwing, it closely approached the morphospace of extant gliding mammals. Addition of a handwing to the model lacking this structure results in a 2.3-fold increase in aspect ratio and a 28% decrease in wing loading, thus greatly enhancing aerodynamics. In the context of these models, the rapid evolution of the chiropteran handwing via genetically-mediated developmental changes appears to have been a key transformation in the hypothesized transition from gliding to flapping in early bats.