Chlorinated poly(vinyl chloride) (CPVC) obtained through a dry chlorination of PVC films or grains can show a heterogeneous repartition of its chlorine atoms because the reaction process is limited by the mass transfer of the chlorine gas in the material. In order to describe the evolution of such a system, a set of coupled equations is derived where only two dimensionless constants have to be determined: K-S, which depends on the solubility of the chlorine gas in the PVC, and K-T, the ratio between the diffusion and the reaction characteristic times. The kinetics of chlorination obtained for the different regimes matches the available experimental data, and the corresponding concentration profiles for the chlorinated PVC chains are displayed to demonstrate how a heterogeneous chlorination can arise from this dual process. In particular, a sharp interface appears in the diffusion-limited regime that separates the chlorinated region from an unchlorinated core and is shown to progress deeper into the film with the square root of time. To a larger extent, this analysis shows how heterogeneity of reaction and nonlinear effects can arise from a coupling between a diffusive phenomenon and a reactive phenomenon.