Ordered one-dimensional C-60 chains on a vicinal Cu template were studied by angle-resolved photoemission. A complete structural model for C-60 on Cu(553) is proposed, where two differently coordinated and oriented C-60 molecules self-assemble in chains along the steps of the vicinal substrate. The highest occupied molecular orbital-derived peak shows a broad Gaussian line shape with features dispersing up to 400 meV along the chains. The line shape is interpreted in terms of a strong electron-phonon interaction leading to the formation of polarons with a spectral function dominated by incoherent multiphonon excitations. The large dispersion of this incoherent peak derives from a particularly favorable relative orientation of the molecules and is in good agreement with the one-electron band structure calculated by density functional theory, which indicates that the photoelectrons carry some memory of the frozen lattice.