In this short note we describe a novel method, based upon the Kirkwood equation, for doing free energy simulations in asymmetric molecular systems typical of those encountered with supercritical fluid mixtures involving large organic species solvated in a lighter supercritical gas. The rationale behind this modified Kirkwood approach has been to develop simulation procedures that are both accurate and stable, by minimizing the perturbation to the system that is implicit to all perturbation-based simulation methods. A good example of an algorithm in this latter class of methods is the free energy perturbation method (FEP) which has been used in this work for comparative purposes with our proposed technique which we refer to as the modified Kirkwood coupling method (MKC). The MKC approach described here effectively makes the perturbation process in the simulation process vanishingly small and appears to result in a stable, accurate algorithm for free energy calculations in chemical mixtures. Numerical results supporting these conclusions are provided in two Lennard-Jones model systems at supercritical conditions.