Na3PS4 is one of the most promising Na+ conductors, relevant for applications that can leverage its high ionic conductivity, such as solid-state batteries. Currently, two crystalline phases of the material have been identified, and it has been thought to melt above 500 °C. In contrast, based on diffraction, ab initio simulations, impedance spectroscopy, and thermal analysis, we show that Na3PS4 remains solid above this temperature and transforms to a third polymorph, γ, exhibiting fast-ion conduction and an orthorhombic crystal structure. We show that the fast Na+-conduction is associated with rotational motion of the thiophosphate polyanions pointing to a plastic crystal. These findings are of major importance for the development and under...