High-mobility perovskite BaSnO3 films are of significant interest as new wide bandgap semiconductors for power electronics, transparent conductors, and as high mobility channels for epitaxial integration with functional perovskites. Despite promising results for single crystals, high-mobility BaSnO3 films have been challenging to grow. Here, we demonstrate a modified oxide molecular beam epitaxy (MBE) approach, which supplies pre-oxidized SnOx. This technique addresses issues in the MBE of ternary stannates related to volatile SnO formation and enables growth of epitaxial, stoichiometric BaSnO3. We demonstrate room temperature electron mobilities of 150 cm2 V−1 s−1 in films grown on PrScO3. The results open up a wide range of opportunities for future electronic devices.