A thermodynamic framework for the analysis of gas sorption in glassy polymers is established in the limit of low sorption levels. The results represent an extension of the Flory-Huggins theory to materials with nonzero internal energy changes due to deformation; the Flory-Huggins theory is recovered in the limit of zero polymer bulk modulus. The sorption isotherm is expressed in terms of the penetrant vapor-phase activity, polymer physical properties, the penetrant partial molar volume, and the heat of mixing. The qualitative form of the isotherm is shown to be unrelated to the presence of excess free volume in the polymer; only quantitative predictions are influenced. The downward curvature of the isotherm is due to the thermodynamics of solid deformation. Explicit relationships between the parameters of this work and the dual-mode model are given for the low-sorption/high-bulk modulus limit.