With hydrogen being seen as a key renewable energy vector, the search for materials exhibiting fast hydrogen transport becomes ever more important. Not only do hydrogen storage materials require high mobility of hydrogen in the solid state, but the efficiency of electrochemical devices is also largely determined by fast ionic transport. Although the heavy alkaline-earth hydrides are of limited interest for their hydrogen storage potential, owing to low gravimetric densities, their ionic nature may prove useful in new electrochemical applications, especially as an ionically conducting electrolyte material. Here we show that barium hydride shows fast pure ionic transport of hydride ions (H-) in the high-temperature, high-symmetry phase. Although some conductivity studies have been reported on related materials previously, the nature of the charge carriers has not been determined. BaH2 gives rise to hydride ion conductivity of 0.2 S cm(-1) at 630 degrees C. This is an order of magnitude larger than that of state-of-the-art proton-conducting perovskites or oxide ion conductors at this temperature. These results suggest that the alkaline-earth hydrides form an important new family of materials, with potential use in a number of applications, such as separation membranes, electrochemical reactors and so on.