This study investigates the ordering effects which occur on the cation sublattice of the CuInS2 compound. CuInS2 is grown on single-crystalline silicon substrates of (001) orientation. The ordered, sulfur-terminated surface Si(001)(1 x 1)-S constitutes well-defined starting conditions for the epitaxial growth process using molecular beams. The silicon surfaces and epitaxial CuInS2, films are characterized in situ by means of Auger electron spectroscopy and low-energy electron diffraction. X-Ray diffraction, and transmission electron microscopy are employed for an ex situ structural characterization. We demonstrate the coexistence of CuAu-type ordering and disorder and a complete absence of the equilibrium chalcopyrite order. CuInS2, with the tetragonal CuAu structure is shown to grow exclusively in c-axis direction.