In this paper we propose a formulation of an optimal resolution problem in supercritical fluid chromatography (SFC) using variational theory. In the recent supercritical fluid literature there has been interest in the enhanced selectivity properties of near-critical fluids used as mobile phases in SFC. As the near-critical thermodynamic retrograde region is traversed, selectivity increases dramatically, often with respect to similar molecular species which are of most interest in separations technology. However, column retention times in the retrograde region tend to be maximal and as a result resolution and speed of processing, both desirable objectives, are in conflict here. The purpose of the optimal control formulation is to resolve this conflict according to a prespecified objective function. The numerical solution of the optimization problem provided here shows that there is significant potential for optimizing system performance. The calculations were done using a molecular thermodynamic model for species adsorption that in our previous experimental work was shown to be accurate for predicting retention time characteristics in SFC columns. Thus the insights gained from this computational study will be useful in future experimental investigations.