Scanning tunneling microscopy (STM) studies of C60 molecules on a Au(110) single crystal surface have been performed in ultrahigh vacuum and at low temperatures (5 and 50 K). Submonolayer, monolayer, and bilayer coverages of C60 have been sublimated onto reconstructed Au(110) 1X2 surfaces. STM images reveal ordered C60 overlayers which are commensurate with the atomic geometry of the substrate. Moreover, we have observed intramolecular patterns within single C60 molecules in unordered and ordered arrays of C60 in the first as well as in the second adsorption layer which may be associated with different orientations of the fullerenes on the highly corrugated gold substrate.