Conventional Li-ion cathodes store charge by reversible intercalation of Li coupled to metal cation redox. There has been increasing interest in new materials capable of accommodating more than one Li per transition-metal center, thereby yielding higher charge storage capacities. We demonstrate here that the lithium-rich layered iron sulfide Li2FeS2 as well as a new structural analogue, LiNaFeS2, reversibly store >= 1.5 electrons per formula unit and support extended cycling. Ex situ and operando structural and spectroscopic data indicate that delithiation results in reversible oxidation of Fe2+ concurrent with an increase in the covalency of the Fe-S interactions, followed by reversible anion redox: 2 S2-/(S-2)(2-). S K-edge spectroscopy unequivocally proves the contribution of the anions to the redox processes. The structural response to the oxidation processes is found to be different in Li2FeS2 in contrast to that in LiNaFeS2, which we suggest is the cause for capacity fade in the early cycles of LiNaFeS2. The materials presented here have the added benefit of avoiding resource-sensitive transition metals such as Co and Ni. In contrast to Li-rich oxide materials that have been the subject of so much recent study and that suffer capacity fade and electrolyte degradation issues, the materials presented here operate within the stable potential window of the electrolyte, permitting a clearer understanding of the underlying processes.