The C60 molecules are known to bind covalently to the Pt(1 1 1) surface. We performed a structural study of one C60 layer on Pt(1 1 1) by using X-ray photoelectron diffraction (XPD). Our results show that the molecules are bonded to the metal surface with their six-carbon rings facing the Pt(1 1 1) surface and with the CC bonds perpendicularly oriented with respect to the direction of the close-packed atom rows. Unlike to what previously found for Cu(1 1 1) and Al(1 1 1), the measured diffraction pattern shows a three-fold symmetry indicating that only one orientation is taken by the chemisorbed molecules. This can be explained by a stronger interaction of the C60 molecules with the second layer Pt atoms.