A nanometer scale dynamical theory is proposed for the large amplitude strain hardening phenomenon in polymer glasses. The new physical picture is that external deformation induces anisotropic chain conformations, which modifies interchain packing, resulting in density fluctuation suppression and intensification of localizing dynamical constraints and activation barriers. The resulting stresses are of intermolecular origin and arise primarily from prolongation of segmental relaxation, not single chain entropic rubber elasticity. Theoretical predictions for the magnitude, temperature, and deformation rate dependence of the hardening modulus are consistent with experiments and simulations.