Image formation in modern lithographic processes is based on the acid-catalyzed deprotection of glassy polymer films. It is well-established that slow acid diffusion controls the reaction kinetics, but models based on Fickian transport cannot describe experimental data. We studied the acid-catalyzed deprotection of glassy poly(hydroxystyrene-co-tertbutyl acrylate) films using infrared absorbance spectroscopy, small angle X-ray scattering, and stochastic simulations. Experimental data were interpreted with a model that explicitly accounts for acid transport, where heterogeneities at local length scales are introduced through a non-exponential distribution of waiting times between successive hopping events. Subdiffusive behavior predicts key attributes of the observed deprotection rates, such as fast reaction at short times, slow reaction at long times, and a non-linear dependence on acid loading. This transport model is remarkably consistent with other literature studies of probe diffusion in inert glasses, which suggests that the same underlying physics (i.e., dynamic heterogeneities) are responsible for the observed anomalous behavior in our reacting system. In our ongoing work, we highlight the complex behavior in photoresists by changing the size of acid-counterion pairs, film thickness, and polymer/substrate interfacial energy. These data can facilitate the development of predictive lithography models that reflect the behavior of confined polymers.