We show that the phenomenon of stochastic resonance exists in the enzymatic peroxidase-oxidase reaction. The free-running system is placed in an excitable steady state close to a supercritical Hopf bifurcation. When a sinusoidal flow rate signal and increasing noise are imposed on this focal steady state and a threshold is crossed, the system responds with the generation of bursts. When stochastic resonance is achieved, the interspike histogram and the plot of the signal-to-noise ratio pass through a maximum at an optimal noise level. We compare the experimental results with calculations of the Hung-Schreiber-Ross model.