Dry Nafion perfluorosulfonate ionomer films incorporating mixed-valent osmium(II/III) tris(4,4’-dimethyl-2,2’-bipyridine) or osmium(II/III) tris(2,2’-bipyridine) are shown to be electronic conductors due to electron self-exchange (hopping) from Os(II) to Os(III) sites. Film conductivity is measured as a function of the product [Os(II)][Os(III)] of site concentrations and conforms to the expected bimolecular rate law. Hopping current-voltage curves are analyzed with a Marcus-based model and the dispersive transport model of Scher, Montroll, and Pfister. The activation energy for electron hopping is 44 +/- 3 kJ/mol, and the bimolecular rate constant is ca. 2 X 10(3) M(-1) s(-1). Exposure to water vapor increases both the ionic and electronic conductivity of the mixed-valent films. Infrared spectra of Os-containing films show evidence of ion pairing between sulfonate and osmium complexes. These observations are consistent with a model in which electron-hopping rates are limited by intersite hop distance in the rigid polymer matrix.