We combine our force-based theory of activated segmental relaxation for glass-forming polymer melts, with our new formulation of how nm-scale effectively static structural fluctuations induce dynamic heterogeneity in molecular liquids, to address the problem of decoupling of the temperature dependence of the segmental and chain relaxation times in supercooled polymer melts. The consequences of two extreme assumptions about how fluctuations of the segmental relaxation time affect chain scale relaxation, and also the influence of quantitative differences of the length scale of structurally heterogeneous domains, are studied. Though these two factors modify our precise quantitative results, they do not change the basic predictions. The highly polymer-specific degree of decoupling is predicted to correlate with the amplitude of collective elastic barrier fluctuations and segmental dynamic fragility. An apparent fractional power law form of the decoupling of the temperature dependence of the segmental and chain relaxation times in the deeply supercooled regime is predicted. The theoretical results appear to be consistent with experimental observations, including both the strong polymer chemistry dependence of the decoupling exponent and the relative insensitivity of chain-scale fragility to the chemical structure.