We present molecular dynamics simulations of a binary Lennard-Jones mixture at temperatures below the kinetic glass transition. The "mobility" of a particle is characterized by the amplitude of its fluctuation around its average position. The 5% particles with the largest/smallest mean amplitude are then defined as the relatively most mobile/immobile particles. We investigate for these 5% particles their spatial distribution and find them to be distributed very heterogeneously in that mobile as well as immobile particles form clusters. We suggest that this dynamic heterogeneity may be due to the fact that mobile/immobile particles are surrounded by fewer/more neighbors which form an effectively wider/narrower cage. The dependence of our results on the length of the simulation run indicates that individual particles have a characteristic mobility time scale which can be approximated via the non-Gaussian parameter.