The molecular ordering of coronene (C24H12) obtained by vacuum-deposition onto predominantly Ag(lll) on mica has been investigated using the scanning tunnelling microscope. Real-space topographic images reveal that in certain regions we obtain layer-by-layer ordered growth of the molecules on this substrate which agrees with previous indirect measurements (the growth did not display this ordering in other regions). In our experiments on the ordered regions, we observe the best imaging contrast at a voltage bias of -0.28 V which may correspond to a resonant tunnelling process through the molecules.