A reaction involving the catalytic oxidation of glucose by the enzyme glucose oxidase is employed as a first spatially resolved experimental realization of a nonclassical A + C --> + Products chemical reaction. This heterogeneous kinetics experiment models the operation of optical glucose sensors. One-dimensional nonclassical reaction kinetics, manifested in anomalous rate laws, are observed. The time evolution of the density gradient of Oz in the zone near the catalytic trap was monitored. The temporal dependence of the growth of this depletion zone M, predicted to scale as t(1/2), was measured to be M similar to t(0.50+/-0.05). This time dependence of the growth in M is directly proportional to the anomalous, time-dependent, reaction rate coefficient.