High-quality lattice images of silicon films grown epitaxially on sapphire substrates directly demonstrate the absence of misfit dislocations at the silicon/sapphire interface. With a point resolution of about 2.5 Å, these images show the absence of lattice faults and detectable strains in the silicon immediately adjacent to the subtrate over interface areas as large as 200 nm in diameter. The incoherent nature of the interface and the absence of misfit dislocations are explained in terms of the chemical bond structure at the interface.