Advanced thermoelectric technology offers a potential for converting waste industrial heat into useful electricity, and an emission-free method for solid state cooling(1,2). Worldwide efforts to find materials with thermoelectric figure of merit, zT values significantly above unity, are frequently focused on crystalline semiconductors with low thermal conductivity(2). Here we report on Cu2-xSe, which reaches a zT of 1.5 at 1,000 K, among the highest values for any bulk materials. Whereas the Se atoms in Cu2-xSe form a rigid face-centred cubic lattice, providing a crystalline pathway for semiconducting electrons (or more precisely holes), the copper ions are highly disordered around the Se sublattice and are superionic with liquid-like mobility. This extraordinary 'liquid-like' behaviour of copper ions around a crystalline sublattice of Se in Cu2-xSe results in an intrinsically very low lattice thermal conductivity which enables high zT in this otherwise simple semiconductor. This unusual combination of properties leads to an ideal thermoelectric material. The results indicate a new strategy and direction for high-efficiency thermoelectric materials by exploring systems where there exists a crystalline sublattice for electronic conduction surrounded by liquid-like ions.