We present a density-functional theory (DFT) study combined with scanning tunneling microscopy (STM) experiments of the chemisorption of the N,N'-bis(1-hexylheptyl) perylene-3,4:9,10-bis(dicarboximide) molecule, noted here as DHH-PTCDI, on the SiC(0001)-3 x 3 surface. Five possible adsorption configurations have been investigated in which molecular adsorption occurs on two adjacent Si adatoms via different pairs of atoms of the molecule. We have calculated the energies, structures, density of states, local density of states, and a calculated STM image and show that chemisorption via two oxygen atoms located on the same side of the molecule on two adjacent Si adatoms is the most favorable, in agreement with the experimental STM images. A comparison between the PTCDI and the adsorption of another large organic molecule (phthalocyanine) on the SiC(0001) surface completes this work.