Molecular simulations of a model, deeply quenched polymeric glass show that the elastic moduli become strongly inhomogeneous at length scales comprising several tens of monomers; these calculations reveal a broad distribution of local moduli, with regions of negative moduli coexisting within a matrix of positive moduli. It is shown that local moduli have the same physical meaning as that traditionally ascribed to moduli obtained from direct measurements of local constitutive behaviors of macroscopic samples.