A powder neutron diffraction study of alpha -AgI has been carried out at several temperatures between 180 degrees C and 450 degrees C. The results do not support the widely quoted model for the distribution of silver ions originally proposed by Strock (1934-36) but instead indicate the silver ions are confined to the twelve tetrahedral sites of the body-centred cubic structure. Remarkably large temperature factors are observed and it is postulated that there is a large anharmonic contribution to the thermal vibrations arising from a reduced energy barrier in the direction of the octahedral sites.