The low temperature kinetics of the reactions of OH with ethanol and propan-2-ol have been studied using a pulsed Laval nozzle apparatus coupled with pulsed laser photolysis-laser-induced fluorescence (PLP-LIF) spectroscopy. The rate coefficients for both reactions have been found to increase significantly as the temperature is lowered, by approximately a factor of 18 between 293 and 54 K for ethanol, and by similar to 10 between 298 and 88 K for OH + propan-2-ol. The pressure dependence of the rate coefficients provides evidence for two reaction channels: a zero pressure bimolecular abstraction channel leading to products and collisional stabilization of a weakly bound OH-alcohol complex. The presence of the abstraction channel at low temperatures is rationalized by a quantum mechanical tunneling mechanism, most likely through the barrier to hydrogen abstraction from the OH moiety on the alcohol.