The epitaxy of a thin-film Y-Ba-Cu-O (YBCO) superconductor deposited on a single-crystal [001] MgO substrate was examined by transmission electron microscopy. The large lattice mismatch (8-10%) in the basal plane of YBCO and MgO is accommodated mainly by the formation of a polycrystalline, mosaic structure. The grain boundaries correspond to unique crystallographic interfaces, determined by the crystal symmetry of the substrate and the thin film.