The microscopic dynamics of protons (H^{+}) in poly(ethylene oxide) (PEO) have been investigated through a study of implanted positive muons (Mu^{+}), which can be considered a light proton analog. The exponential decay of the muon spin polarization in zero magnetic field indicated that Mu^{+} hopping is in the fast fluctuation limit between 140 and 310 K and the relaxation rate was found to be sensitive to the glass transition. Mu^{+} dynamics in PEO was monitored via the relaxation of the muon spin polarization in a transverse field of 10 mT. Activated hopping of Mu^{+} was observed above the glass transition temperature with an activation barrier of 122±1 meV. The temperature dependence of the diamagnetic muon polarization in PEO can be explained by diffusion of radiolytic electrons.