Multiple quantum well structures consisting of alternating layers of two crystalline organic semiconductors, namely, 3,4,9,10 perylenetetracarboxylic dianhydride (PTCDA) and 3,4,7,8 naphthalenetetracarboxylic dianhydride (NTCDA), have been grown by organic molecular beam deposition. The layer thickness was varied from 10 to 200 Å. Birefringence measurements indicate that there is a strong structural ordering in all PrCDA layers, although the PrCDA and NTCDA crystal structures are incommensurate. From optical absorption measurements, it is found there is a blue shift in the lowest energy PICDA singlet exciton line with decreasing layer thickness. A model based on exciton quantum confinement is proposed to explain the energy shift. We have measured the low temperature photoluminescence spectra of organic quantum well structures, and found a slight red shift in the spectra with decreasing well width. These results are also discussed.