When a neutral nonelectrolyte is added to an electrolytic solution, the electrical conductance of the electrolytic solution is usually reduced. Attempts to correlate this effect with changes in the bulk properties of the solvent have been unsuccessful. The purpose of this paper is to account for this effect (for dilute solutions) in terms of a statistical mechanical theory which takes into account the specific interactions between molecules of the nonelectrolyte and ions of the electrolyte. A simple continuum model is used to represent the solution containing nonelectrolyte molecules and electrolyte ions placed in a constant, homogeneous electric field. With an approximate theory valid at infinite dilution, an equation describing the variation of the limiting equivalent conductance of the electrolyte with the concentration of an ideal dipolar nonelectrolyte is obtained. Comparisons with experiments are made.