This Letter presents the high-resolution C 1s near-edge X-ray absorption fine structure (NEXAFS) spectra of hydrogenated and deuterated polystyrene. The differences between these spectra provide unambiguous evidence for the presence of a significant vibronic contribution to the shape and structure of the C 1s(C-H) --> 1 pi*(C=C) transition in polystyrene. High-resolution NEXAFS spectra, spectroscopic simulations and ab initio calculations are used to help resolve the relative contributions of chemical shifts and vibronic excitation to the shape of the characteristic C 1s(C-H) --> 1 pi*(C=C) transition.