We demonstrate the making of BaZrS3 thin films by molecular beam epitaxy (MBE). BaZrS3 forms in the orthorhombic distorted-perovskite structure with corner-sharing ZrS6 octahedra. The single-step MBE process results in films smooth on the atomic scale, with near-perfect BaZrS3 stoichiometry and an atomically-sharp interface with the LaAlO3 substrate. The films grow epitaxially via two, competing growth modes: buffered epitaxy, with a self-assembled interface layer that relieves the epitaxial strain, and direct epitaxy, with rotated-cube-on-cube growth that accommodates the large lattice constant mismatch between the oxide and the sulfide perovskites. This work sets the stage for developing chalcogenide perovskites as a family of semiconductor alloys with properties that can be tuned with strain and composition in high-quality epitaxial thin films, as has been long-established for other systems including Si-Ge, III-Vs, and II-Vs. The methods demonstrated here also represent a revival of gas-source chalcogenide MBE.