In oxides, the substitution of non-oxide anions (F-, S2-, N3- and so on) for oxide introduces many properties, but the least commonly encountered substitution is where the hydride anion (H-) replaces oxygen to form an oxyhydride. Only a handful of oxyhydrides have been reported, mainly with electropositive main group elements(1-5) or as layered cobalt oxides with unusually low oxidation states(6,7). Here, we present an oxyhydride of the perhaps most well-known perovskite, BaTiO3, as an O2-/H- solid solution with hydride concentrations up to 20% of the anion sites. BaTiO3-xHx is electronically conducting, and stable in air and water at ambient conditions. Furthermore, the hydride species is exchangeable with hydrogen gas at 400 degrees C. Such an exchange implies diffusion of hydride, and interesting diffusion mechanisms specific to hydrogen may be at play. Moreover, such a labile anion in an oxide framework should be useful in further expanding the mixed-anion chemistry of the solid state.