An improvement of lithium-ion batteries with regard to their reversible capacity, cycling stability, rate performance, and safety under repetitive charge and discharge still requires considerable research activity. However, graphite has remained the unexcelled material for the anode so far. Here, it is shown that two novel quaternary lithium-chalcogenidometalate phases, Li4MnGe2S7 (1) and Li4MnSn2Se7 (2), represent very promising new anode materials for lithium-ion cells in that they achieve specific lithium storage capacities higher than that of the commercially used graphite, and display an excellent stability during cycling. These properties are based on the structural peculiarities of the phases, which adopt Wurtzite-related topologies and provide high structural flexibility of the metal sulfide or selenide bonds as advantageous pre-requisitions for a large ion accessible volume.