We report a molecular dynamics study of pairing and dynamics of lithium cation and perchlorate anion in a previously reported model of amorphous polyethylene oxide. We are particularly interested in the question of whether these ions pair in the model, as previously reported experimentally. We calculate the potential of mean force between a lithium and perchlorate ion in the system for several temperatures when a pair of ions is at various separation distances in our model. We find evidence for two minima in the potential of mean force, one at lithium-chlorine separations of 3.5 Å and about 6.5 Å. We studied the same system with five ion pairs in the system and again find two minima at the same separation distances but in this case there is evidence of entropic effects in the binding free energy of the pairs at 3.5 Å. A study of radial distribution functions permits us to deduce information concerning the structure of the paired states.