The enzymatic degradation of recalcitrant plant biomass is one of the key industrial challenges of the 21st century. Accordingly, there is a continuing drive to discover new routes to promote polysaccharide degradation. Perhaps the most promising approach involves the application of "cellulase-enhancing factors," such as those from the glycoside hydrolase (CAZy) GH61 family. Here we show that GH61 enzymes are a unique family of copper-dependent oxidases. We demonstrate that copper is needed for GH61 maximal activity and that the formation of cellodextrin and oxidized cellodextrin products by GH61 is enhanced in the presence of small molecule redox-active cofactors such as ascorbate and gallate. By using electron paramagnetic resonance spectroscopy and single-crystal X-ray diffraction, the active site of GH61 is revealed to contain a type II copper and, uniquely, a methylated histidine in the copper's coordination sphere, thus providing an innovative paradigm in bioinorganic enzymatic catalysis.