We investigated the adsorption properties and self-assembly of rubrene molecules on the copper oxide nanotemplate formed by high-temperature exposure of Cu(110) to molecular oxygen. Using high-resolution scanning tunneling microscopy under ultrahigh-vacuum conditions, we observed a complex variety of self-assembled motifs, driven by competing effects such as the chemical affinity between the organic molecule and the surface, surface coverage, and spatial confinement of the rubrene molecules within the rows of the template.