Single crystal heteroepitaxial ferroelectric films are desired for non-linear optical applications to maximize the electro-optic coefficient and minimize waveguide losses. In this study, lithium tantalate films were deposited on (0001) sapphire from lithium hexaethoxytantalate by chemical beam epitaxy. Characterization showed that films had nearly stoichiometric composition, epitaxial orientation, and a high degree of crystalline perfection. However, the films exhibited high optical waveguide losses. Additional characterization by TEM revealed that the films had a two dimensional grain structure with epitaxial variants related by translation and a twin orientation to the substrate. To better understand the nature of the heteroepitaxial growth of lithium tantalate on (0001) sapphire, a model was developed to explain the observed epitaxial orientations, misfit dislocation networks, and grain boundary structures of lithium tantalate on (0001) sapphire.