A model of the peroxidase-oxidase (PO) reaction which explicitly includes the species 2,4-dichlorophenol (DCP) is proposed. Simulations with this model are run at different pH values, resulting in mixed-mode oscillations at pH = 6.3, which go through period-doubling bifurcations into chaos, in agreement with recent experimental reports of studies at the higher pH. The dependence of features of these oscillations on NADH feedstream concentration and DCP initial concentration is also explored. Finally, comparison of detailed features of the simulated strange attractor to the recent experimental attractor reveals minor differences which may turn out to be important in elucidating the role of DCP in the mechanism which leads to chaos in the PO reaction.