Owing to its high room-temperature electron mobility and wide bandgap, BaSnO 3 has recently become of significant interest for potential room-temperature oxide electronics. A hybrid molecular beam epitaxy (MBE) approach for the growth of high-quality BaSnO 3 films is developed in this work. This approach employs hexamethylditin as a chemical precursor for tin, an effusion cell for barium, and a radio frequency plasma source for oxygen. BaSnO 3 films were thus grown on SrTiO 3 (001) and LaAlO 3 (001) substrates. Growth conditions for stoichiometric BaSnO 3 were identified. Reflection high-energy electron diffraction (RHEED) intensity oscillations, characteristic of a layerby-layer growth mode were observed. A critical thickness of $1 nm for strain relaxation was determined for films grown on SrTiO 3 using in situ RHEED. Scanning transmission electron microscopy combined with electron energy-loss spectroscopy and energy dispersive x-ray spectroscopy confirmed the cube-on-cube epitaxy and composition. The importance of precursor chemistry is discussed in the context of the MBE growth of BaSnO 3. V