The ideal adsorbed solution (IAS) theory of adsorption of gas mixtures is extended to the case of energetic heterogeneity. A heterogeneous ideal adsorbed solution (HIAS) behaves ideally on a particular site, but energetic heterogeneity causes a segregation in the composition of the adsorbed phase. Equilibrium properties are obtained by integrating over a multivariate energy distribution based upon perfect positive correlation of site energies. The fact that predictions from HIAS are always an improvement over IAS indicates that heterogeneity is a factor that must be considered in theories of mixed-gas adsorption. Errors in HIAS predictions may be caused by steric exclusion of the larger molecules from micropores accessible to smaller molecules.