A thin film of copper on the fivefold surface of Al-Pd-Mn forms a structure that is uniaxially commensurate with the aperiodic structure of the substrate. This structure has been analyzed using low-energy electron diffraction and is found to consist of a vicinal surface of a body-centered tetragonal (bct) (100) structure. This bct(100) structure has lattice parameters of a = 2.88 Å, b = 2.55 Å and c = 2.88 Å, with the vicinal surface making an angle α of 13.28° relative to the a-b plane. This structure provides an explanation for the delayed ordering observed during the growth of the film. Simple conditions are derived for which the growth of ordered one-dimensionally quasiperiodic thin films on quasicrystals may be favorable. This finding is relevant to the use of quasicrystals as a means of matching interfaces in thin film systems.