Gold clusters ranging in diameter from 1 to 6 nanometers have been prepared on single crystalline surfaces of titania in ultrahigh vacuum to investigate the unusual size dependence of the low-temperature catalytic oxidation of carbon monoxide. Scanning tunneling microscopy/spectroscopy (STM/STS) and elevated pressure reaction kinetics measurements show that the structure sensitivity of this reaction on gold clusters supported on titania is related to a quantum size effect with respect to the thickness of the gold islands; islands with two layers of gold are most effective for catalyzing the oxidation of carbon monoxide. These results suggest that supported clusters, in general, may have unusual catalytic properties as one dimension of the cluster becomes smaller than three atomic spacings.