We studied the local chain dynamics as well as the dynamic heterogeneity in highly cross-linked epoxy near glass transition by molecular dynamics simulation. In previous work (Lin and Khare in Macromolecules 2009, 42, 4319), we had reported creation of fully relaxed atomistic structures of cross-linked epoxy; the glass transition temperature of these structures was also determined from volume-temperature behavior. The local chain dynamics in these structures is characterized by using molecular dynamics simulation in this work. Local translational mobility of cross-linked epoxy as measured by mean-squared displacement of atoms exhibited two subdiffusive regimes within the simulation time of 200 ns. Local orientational mobility was determined by monitoring the autocorrelation function (ACF) of a vector associated with the epoxy monomer. Time dependence of an order parameter based on this ACF showed that there was almost no orientational relaxation when the temperature was near or below glass transition temperature and the system cannot completely relax orientationally even at temperatures that are 120 K higher than the glass transition temperature. Furthermore, a time scale for the identification of glass transition in simulations was determined using the kinetic interpretation of glass transition. Dynamic heterogeneity was studied by identifying the mobile and immobile atoms in the system. Simulation results confirmed the existence of dynamic heterogeneity in the cross-linked system with the fraction of the immobile domains in the structures showing a rapid increase as the temperature dropped below the glass transition temperature. Results are also presented for the probability of percolation of the system by the immobile domains in the vicinity of glass transition.