The structure of copper phthalocyanine (CuPc) thin films (5-100 nm) deposited on single-crystal ZnO(1 (1) over bar 00) substrates by organic molecular beam deposition was determined from grazing-incidence X-ray diffraction reciprocal space maps. The crystal structure was identified as the metastable polymorph alpha-CuPc, but the molecular stacking was found to vary depending on the film thickness: for thin films, a herringbone arrangement was observed, whereas for films thicker than 10 nm, coexistence of both the herringbone and brickstone arrangements was found. We propose a modified structure for the herringbone phase with a larger monoclinic beta angle, which leads to intrastack Cu-Cu distances closer to those in the brickstone phase. This structural basis enables an understanding of the functional properties (e.g., light absorption and charge transport) of (opto)electronic devices fabricated from CuPc/ZnO hybrid systems.