Precisely controlled fabrication of low-dimensional molecular structures with tailored morphologies and electronic properties is at the heart of the nanotechnology research. Especially, the formation of one-dimensional (1D) structures has been strongly desired due to their expected high performance for information processing in electronic/magnetic devices. So far, however, they have been obtained by tough and slow methods such as manipulation of individual molecules, which are totally unsuited for mass production. Here we show that highly ordered cobalt-phthalocyanine chains can be self-assembled on a metal surface using fractional atomic steps as a template. We also demonstrate that the substrate surface electrons, which can be confined by cobalt-phthalocyanine molecules, can propagate along the step arrays and can hybridize with the molecular orbitals. These findings provide a significant step toward readily realization of 1D charge/spin transport, which can be mediated either directly by the molecules or by the surface electrons.