Hydrogen transport in solids is of scientific interest, and also technological importance, because of the role of hydrogen-permeable membranes in fuel cells.[1] There has therefore been considerable interest in the mobility of protons in transition-metal oxides. The existence of negatively charged hydrogen species (hydrides) in ionically conducting oxides at low oxygen partial pressures has been suggested (e.g., in SrTiO 3 ) together with their possible role in ionic transport.[2] We recently prepared the first example of a transition-metal oxide hydride, LaSrCoO 3 H 0.7, in which the hydride species replace some of the oxide anions in their role of linking the metal cations.[3] Neutron scattering measurements have revealed the dynamics of proton transport in perovskite proton conductors, but no quantitative information on the mobility of hydride species in oxides is available. Recent reports on the novel oxide hydride LaSrCoO 3 H 0.7 have posed important questions about the nature of hydride insertion into LaSrCoO 4 .[4] The LaSrCoO 3 H 0.7 structure is related to the n = 1 member of the A n+1 B n O 3n+1 family of oxides, containing rocksalt (La/Sr)O layers separated by rectangular perovskite (La/Sr)CoO 2 H 0.7 layers (Fig. 1). When hydride anions are substituted for oxide anions in the tetragonal LaSrCoO 4 starting material, a rectangular distortion occurs in the plane of the perovskite layer, producing a longer axis (a = 3.87 Å) along the O-Co-O direction and a shorter axis (b = 3.60 Å) along the H-Co-H direction. [4] LaSrCoO 3 H 0.7 is formed by a novel chimie-douce (soft chemistry) reaction between CaH 2 and LaSrCoO 4 . A combination of in situ and ex situ powder X-ray diffraction has been used to propose a mechanism that involves the reduction of LaSrCoO 4 to the reduced intermediate LaSrCoO 3.5-x , followed by insertion of the hydride anion, rather than reducing the cobalt cation to the metal as might be expected. The mobility of the hydride anion in the lattice is therefore an issue of particular importance in the synthesis of the oxide hydride, as its presence must contribute to the stability of the phase in the highly reducing synthetic environment. Further studies on the mechanism of hydride insertion are warranted by the lack of such information on any known oxide hydride material, including LaHO, [5] Ba 3 (AlO 4 )H, [6] Ba 21 Ge 2 O 5 H 24 , [7] and BaMnO 3 H 3 .[8] Quasielastic neutron scattering (QENS) is a well-established technique for probing diffusion of atoms and molecules in such systems as proton-conducting oxides, [9] metal-hydride systems, [10] ionic polymers, [11] and clay minerals. [12] We report herein that hydride anion mobility within the perovskite layer of LaSrCoO 3 H 0.7 above 675 K has been observed by high-resolution QENS; the observed diffusion allows an estimate of the molar hydride ion conductivity as being on the order of 4 S cm -1 .Quasielastic broadening associated with the onset of hydride ion motion in LaSrCoO 3 H 0.7 has been detected above a temperature of 675 K (Fig. 2...