Stabilization of the Si(553) surface by Au adsorption results in two different atomically defined chain types, one of Au atoms and one of Si. At low temperature these chains develop two- and threefold periodicity, respectively, previously attributed to Peierls instabilities. Here we report evidence from scanning tunneling microscopy that rules out this interpretation. The ×3 superstructure of the Si chains vanishes for low tunneling bias, i.e., close the Fermi level. In addition, the Au chains remain metallic despite their period doubling. Both observations are inconsistent with a Peierls mechanism. On the contrary, our results are in excellent, detailed agreement with the Si(553)-Au ground state predicted by density-functional theory, where the ×2 periodicity of the Au chain is an inherent structural feature and every third Si atom is spin polarized.