D/H exchange between methane and a zeolite is the simplest reaction between a zeolitic proton and a hydrocarbon. Because of its simplicity, it offers a unique opportunity to test out possibilities that are offered by present-day computational techniques to obtain theoretical insight into the catalytic action of zeolites and to test theory against experiment. We report the results of an nb initio quantum chemical study of the D/H exchange process between CD4 and a zeolitic cluster. Within this framework, a relation is established between acidity and the height of the barrier for exchange. This allows for the estimation of differences in the exchange barrier between various zeolites, of which HY (FAU) and HZSM-5 (MFI) are explicitly considered. Transition state theory is used to quantitatively predict the rate constant of the exchange process. The results compare favorably with D/H exchange experiments that have recently been performed.