The structure of monolayer films of copper phthalocyanine (CuPc) deposited on a Au(111) surface in ultrahigh vacuum is studied using scanning tunneling microscopy and low-energy electron diffraction. CuPc molecules adsorb with their molecular plane parallel to the surface and form a highly ordered overlayer with a square unit cell. On terraces wider than similar to 15 nm, the orientation of the monolayer is determined by the underlying substrate and the sides of CuPc square unit cells coincide very closely with the [11 (2) over bar] and [1 (1) over bar 0] directions of the Au(111) surface. On narrow terraces; the sides of the CuPc unit cells are aligned along the step edges. This effect is explained in terms of the maximization of coverage which favors the formation of the CuPc domains where the molecules are aligned parallel to the step edges.