The organic molecule 3,4,9,10-perylene-tetracarboxylic dianhydride (PTCDA) was studied by means of scanning tunneling microscopy (STM) on thin insulating NaCl films grown on a Cu(111) single crystal. The deposition of approximately two monolayers (ML) of sodium chloride onto a Cu(111) substrate at a sample temperature of about 350 K causes a rather rough growth of (100)-oriented NaCl islands up to a local height of 4 ML. For submonolayer coverages (0.1 and 0.4 ML) of PTCDA on a Cu(111) surface partly covered with NaCl, two different rod structures of PTCDA were found on the copper surface, which are in contrast to previously published data for PTCDA on Cu(111) showing a herringbone-like arrangement. These findings can be explained by the formation of a Na(x)-PTCDA complex. On NaCl covered areas, single PTCDA molecules adsorb at vacancies of [010] and [001] oriented steps of the NaCl(100) islands. In this case, the electrostatic forces between the polar step edges and the PTCDA molecules are dominant. The terraces of the alkali halide surface are free of PTCDA molecules.