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The carbon 1s photoelectron spectrum of ethane, C2H6, has been measured at a photon energy of 329 eV and an instrumental resolution of 70 meV. The spectrum shows a rich vibrational structure which is resolved using least-squares fits to the data. Only C-H stretching and CCH bending modes contribute significantly to the spectrum. The lack of excitation of the C-C stretching mode is explained in terms of changes in hybridization at the spectator carbon. To investigate the possibility of incomplete localization of the core hole, the spectra of C2H6 and C2D6 were measured at higher experimental resolution (35 meV). The spectra are accurately fit by a model based on ab initio calculations of the vibrational energies and the geometry changes following ionization, and including vibronic coupling of the two degenerate, localized hole states. A small splitting on the order of 10-20 meV is found for the 2A2u and 2A1g core-ionized states.