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Hexagonal boron nitride (hBN) has been grown on sapphire substrates by ultrahigh-temperature molecular beam epitaxy (MBE). A wide range of substrate temperatures and boron fluxes have been explored, revealing that high crystalline quality hBN layers are grown at high substrate temperatures, >1600℃ , and low boron fluxes, ∼1 × 10%& Torr beam equivalent pressure. In situ reflection high-energy electron diffraction revealed the growth of hBN layers with 60° rotational symmetry and the [112+ 0] axis of hBN parallel to the [11+ 00] axis of the sapphire substrate. Unlike the rough, polycrystalline films previously reported, atomic force microscopy and transmission electron microscopy characterization of these films demonstrate smooth, layered, few-nanometer hBN films on a nitridated sapphire substrate. This demonstration of high-quality hBN growth by MBE is a step toward its integration into existing epitaxial growth platforms, applications, and technologies.