A polymer electrolyte membrane (PEM) fuel cell model that incorporates chemical degradation in perfluorinated sulfonic acid membranes is developed. The model is based on conservation principles and includes a detailed description of the transport phenomena. A degradation submodel describes the formation of hydrogen peroxide via distinct mechanisms in the cathode and anode, together with the subsequent formation of radicals via Fenton reactions involving metal-ion impurities. The radicals participate in the decomposition of reactive end groups to form carboxylic acid, hydrogen fluoride, and CO2. Degradation proceeds through unzipping of the polymer backbone and cleavage of the side chains. Simulations are presented, and the numerical code is shown to be extremely time-efficient. Known trends with respect to operating conditions are qualitatively captured, and the exhibited behavior is shown to be robust to changes in the rate constants. The feasibility of a chemical degradation mechanism based on peroxide and radical formation is discussed.