Organic molecules, designed to have an asymmetrical double-well potential for two protons, were synthesized. The structure allows the switching of the position of the protons by an electric field. A monolayer of these molecules was chemically bound to a surface of gold. A scanning tunneling microscope was modified so that the current-voltage characteristics between the tip and a surface could be obtained rapidly, making it possible to observe the effects of single molecules. Whereas bare Au had usual tunneling characteristics, it was found that the surface with molecules had regions where the I-V was highly asymmetric. For negative voltages there was a switching threshold, beyond which the conductivity was much higher than when the tip was positive. A tentative explanation of the switching and rectification, based on the asymmetry of the molecule, is proposed. © 1988.