Using time-resolved fluorescence, we have measured the direct proton transfer reaction between a photoacid, 2-naphthol-6-sulfonate, and a base, acetate anion, in water-glycerol mixtures. The reaction shows clear evidence for irreversible diffusion-controlled reactivity in agreement with the Smoluchowski model. As the solution viscosity increases, from about 1 cP (neat water) to 40 cP at 0.4 mole fraction of glycerol, the initial ROH* fluorescence decay becomes increasingly nonexponential, providing clear evidence for the transient regime of the Smoluchowski model for a real chemical reaction.