A responsible approach to the development of alternative energy sources, storage and conversion systems is to utilize abundant materials, with minimal or no negative environmental impacts. Here we report that lepidocrocite (γ-FeOOH, a naturally occurring metastable phase of iron oxyhydroxide) shows great promise as a proton conductor, based on sophisticated first-principles calculations that include the important corrections of on-site Coulomb interactions for this strongly correlated material. Our results show how proton transfer is facilitated by phonon vibration modes and relatively low transition energy barriers.