Close-packed Co-Cu chains of various length and composition were assembled from single Co and Cu atoms on Cu(111) by atom manipulation in a low-temperature scanning tunneling microscope. Local spectroscopy reveals significant electronic Co-Cu coupling leading to confined quantum states delocalized along the heteroatomic chain. Composite Co-Cu chains provide a model case in which the quantum state of an atomic-scale host structure can be tuned by the controlled incorporation of foreign atoms.