We derive an asymptotic theory of laminar premixed flames in high density fluids in the limit of large activation energy. The model is intended to provide insights into the structure and dynamics of deagration waves in high pressure, dense fluids where nor- mal Fickian diffusion is limited. In such cases, particularly under conditions exceeding the thermodynamic critical point of the fluid, the primary mode of species transport is through cross-diffusion, i.e. the Soret effect. Such a model for diffusive transport is considered, and we derive a model with an explicit dependence on the Soret effect for a one-step overall reaction. The density is assumed sufficiently high to adopt a constant density formulation. The local reaction-diffusion structure is found to be fundamentally different from that of an ideal gas with Fickian diffusion, which results in new conditions relating the equations for thermal and mass transport in the bulk flow. The model is used to investigate the basic structure of planar flames, as well as their stability. Stability boundaries are identified that mark the transition from planar to either steady, spatially periodic structures, or time-dependent modes of propagation. The combined effects of the Soret diffusion coefficient and Lewis number are discussed.