beta-Detected nuclear spin relaxation of Li-8(+) has been used to study the microscopic diffusion of lithium ions in thin films of poly(ethylene oxide) (PEO), where the implanted lithium ions are present in extremely low concentration, and PEO with 30 wt % LiCF3SO3 over a wide range of temperatures both above and below the glass transition temperature. Recent measurements by Do et al. [Phys. Rev. Lett. 2013, 111, 018301] found that the temperature dependence of the Li+ conductivity was identical to that of the dielectric a relaxation and was well described by the Vogel-Fulcher-Tammann relation, implying the a relaxation dominates the Li+ transport process. In contrast, we find the hopping of Li+ in both samples in the high temperature viscoelastic phase follows an Arrhenius law and depends significantly on the salt content. We propose that the hopping of Li+ between cages involves motion of the polymer but that it is only for long-range diffusion where the alpha relaxation plays an important role.