Recently we reported on a period doubling route to chaos in the peroxidase-oxidase (PO) reaction. This was the first report of a universal route to chaos in the PO reaction. Here we present further evidence of universality in the transition to chaos in the PO reaction. We have observed period three oscillations under conditions near where chaotic oscillations are found, and we have found that chaotic oscillations in this reaction contain unstable periodic orbits. We also report numerical results from a simple model of the PO reaction. These theoretical calculations qualitatively reproduce the spectrum of behaviors observed in this reaction.