We observe the formation of thin films of fibre-like aggregates from the prototypical organic semiconductor molecule para-hexaphenylene (p-6P) on graphite thin flakes and on monolayer graphene. Using atomic force microscopy, scanning electron microscopy, x-ray diffraction, polarized fluorescence microscopy, and bireflectance microscopy, the molecular orientations on the surface are deduced and correlated to both the morphology as well as to the high-symmetry directions of the graphitic surface: the molecules align with their long axis at ±11° with respect to a high-symmetry direction. The results show that the graphene surface can be used as a growth substrate to direct the self-assembly of organic molecular thin films and nanofibres, both with and without lithographical processing.