We derive the differential equations governing the simple distillation of mixtures with multiple equilibrium chemical reactions. The results are most conveniently expressed in terms of transformed composition coordinates, which provide a reduction of dimensionality consistent with the Gibbs phase rule. The resulting residue curve maps give an easy visualization of the combined phase and chemical equilibria, and from them it is possible to determine the presence of reactive azeotropes, as well as nonreactive azeotropes that survive the reactions. Three examples are described : an ideal mixture based on the chemistry of formaldehyde + water, the synthesis of MTBE in the presence of inert n-butane, and the alkylation of m-xylene in the presence of inert p-xylene.