The diffusion of hydride anions in LaSrCoO3H0.7 is measured for the first time. High-resolution quasielastic neutron scattering (QENS) data reveals the onset of mobility above 675 K, associated with hopping between vacant sites in the hydride anion sublattice (see figure). The temperature range at which hopping takes place is similar to the temperature used for the synthesis of the material, and is associated with loss of hydrogen gas from the sample.