Through single-step solid-state reactions, a series of novel bichalcogenides with the general composition (Li2Fe)ChO (Ch = S, Se, Te) are successfully synthesized. (Li2Fe)ChO (Ch = S, Se) possess cubic anti-perovskite crystal structures, where Fe and Li are completely disordered on a common crystallographic site (3c). According to Goldschmidt calculations, Li+ and Fe2+ are too small for their common atomic position and exhibit large thermal displacements in the crystal structure models, implying high cation mobility. Both compounds (Li2Fe)ChO (Ch = S, Se) were tested as cathode materials against graphite anodes (single cells); They perform outstandingly at very high charge rates (270 mA g-1, 80 cycles) and, at a charge rate of 30 mA g-1, exhibit charge capacities of about 120 mA h g-1. Compared to highly optimized Li1-xCoO2 cathode materials, these novel anti-perovskites are easily produced at cost reductions by up to 95% and, yet, possess a relative specific charge capacity of 75%. Moreover, these iron-based anti-perovskites are comparatively friendly to the environment and (Li2Fe)ChO (Ch = S, Se) melt congruently; the latter is advantageous for manufacturing pure materials in large amounts.