When Cu phthalocyanine molecules are chemically bound to graphite surfaces, the tunneling currents of a scanning tunneling microscope becomes much more unsymmetrical than with pristine graphite surface. An explanation of this rectification, in terms of the energy levels of the molecules and the unsymmetrical location of the molecules between the tip and substrate, is offered. The method used for chemical bonding may have wide application for the attachment of molecules to graphite surfaces.