Ion-current measurements were made on synthetic polymer membranes that contained a single conically shaped nanopore. This entailed placing an electrolyte solution on either side of the membrane, using an electrode placed in each solution to control the transmembrane potential, and measuring the resulting transmembrane ion current. The effect of the crown ether commonly called 18-crown-6 (18C6) on the measured ion current was investigated. Adding 18C6 to the electrolyte solution on one side of a conical nanopore membrane provides a way to rectify the ion current flowing through the nanopore. This chemical rectification is observed only when the cation of the electrolyte is complexed by 18C6 (e.g., K+), and when the mouth diameter of the conical nanopore is of molecular dimensions, in this case similar to 1.5 nm. This chemical rectification can either augment or diminish the inherent electrostatic rectification observed with these small mouth-diameter nanopores. We have interpreted these results using a model based on the formation of a junction potential at the membrane-solution interface. This junction potential arises because the transference number for the K+-18C6 complex in bulk solution is larger than its transference number in the mouth of the conical nanopore.