Positron annihilation lifetime spectroscopy, which is applied to measure distributions of hole volume sizes in polymers, uses a model to relate the positronium (Ps) lifetime to hole volume dimensions. It is assumed in this model that the Ps remains in one site until annihilation. Recently, the validity of this last assumption has been questioned by Yu et al. (Yu, Z.; McGervey, J. D.; Jamieson, A. M.; Simha, R. Macromolecules 1995, 28, 6268.), who calculated the tunneling rate between sites and concluded that the rate was rapid enough that a Ps would typically sample many hole volumes before annihilating. To investigate this question we calculated the rate for Ps in one potential well to transfer to a second. We found for appropriate, equal wells, that the rate is comparable with that of Yu et al., while for only slightly unequal wells the transfer is cut off. This cutoff is a consequence of the removal of the degeneracy of the single well energies. For multiple wells it is found that Anderson localization applies so that quite generally a Ps is trapped at only a single hole volume until it decays. Thus Ps-lifetime hole-size-distribution measurements should be unaffected by tunneling.