Using molecular dynamics simulations of a generic model, we observe strain hardening in highly cross-linked polymer glasses under tensile deformation. We show that formation of microvoids, without bond breaking, constitutes the microscopic origins of strain hardening. A well-defined functional form is observed for the void size distribution that is consistent with voids in dense equilibrium Lennard-Jones particle packings, independent of strain. Microvoid-based strain hardening is not observed in a separate model with tetrahedral bond angle constraints, indicating that flexible cross-linkers are the key factor in the development of strain hardening behavior.