Graphene has long been recognized as a potential replacement for indium tin oxide as a transparent conducting substrate that may not only be cheaper to manufacture but also may provide mechanical flexibility and templating for preferential organic film growth. Here, we report the discovery that the thin film growth mode and crystal structure of copper phthalocyanine (CuPc), a prototype organic semiconductor, is extremely sensitive to even atomic-scale defects (e.g., steps) on the graphene surface and that high quality films can be grown with a well-defined crystal orientation that should be favorable for optimized solar cell applications. The initial growth involves flat-lying copper phthalocyanine molecules in a triclinic brickstone crystal with (012̅ ) orientation. Thicker films on pristine graphite, as well as thin films on lower quality graphene, show an orientational transition to the flat-lying (112̅ )-oriented brickstone, which nucleates near film defects and grows in more compact 3D islands. The thickness dependent transition between these two flat-lying crystal orientations is sensitive to substrate defect density since this determines the extent to which initial island elongation along the substrate can alleviate strain in the film. The sensitivity of copper phthalocyanine film morphology demonstrates the extreme importance of graphene substrate quality to controlling organic film growth. The high crystallinity and optimal molecular orientation achieved here implies a new driving force for high performance organic optoelectronics based on substrate-controlled crystal engineering.