Building on the good thermoelectric performances of binary superionic compounds like Cu2Se, Ag2Se and Cu2S, a better and more detailed understanding of phonon-liquid electron-crystal (PLEC) thermoelectric materials is desirable. In this work we present the thermoelectric transport properties of the compound Cu7PSe6 as the first representative of the class of argyrodite-type ion conducting thermoelectrics. With a huge variety of possible compositions and high ionic conductivity even at room temperature, the argyrodites represent a very good model system to study structure-property relationships for PLEC thermoelectric materials. We particularly highlight the extraordinary low thermal conductivity of Cu7PSe6 below the glass limit, which can be associated with the molten copper sublattice leading to a softening of phonon modes.