The adsorption of coronene molecules (C24H12) on the Ge(001) surface has been studied by means of scanning tunnelling microscopy (STM). Upon room temperature deposition, the coronene molecules adsorb in an upright geometry forming compact layers patterned in rows for coverages of one monolayer and less, being the only example investigated so far in which a pure aromatic hydrocarbon forms a well-ordered monolayer on a nonpassivated semiconductor surface. At half monolayer, the molecular rows consist of long chains of pi-stacked molecules and the distance between molecular planes is 8 angstrom. This configuration is maintained upon cooling the system below the transition temperature of Ge(001) (similar to 220 K), but the molecular layer experiences also a transition from rows perpendicular to rows parallel to the Ge dimer rows. We interpret our observations in terms of a weak bonging between molecules and substrate, which facilitates the formation of large ordered domains of molecules, revealing Ge(001) as an ideal template for the growth of this and other aromatic hydrocarbons.