The kinetics of the reaction between O atoms and OH radicals, both in their electronic ground state, have been investigated at temperatures down to ca. 39 K. The experiments employed a CRESU (Cinetique de Reaction en Ecoulement Supersonique Uniforme) apparatus to attain low temperatures. Both reagents were created using pulsed laser photolysis at 157.6 nm of mixtures containing H2O and O-2 diluted in N-2 carrier gas. OH radicals were formed by both direct photolysis of H2O and the reaction between O(D-1) atoms and H2O. O(P-3) atoms were formed both as a direct product of O-2 photolysis and by the rapid quenching of O(ID) atoms formed in that photolysis by N-2 and O-2. The rates of removal of OH radicals were observed by laser-induced fluorescence, and concentrations of O atoms were estimated from a knowledge of the absorption cross-section for O-2 at 157.6 nm and of the measured fluence from the F-2 laser at this wavelength. To obtain a best estimate of the rate constants for the O + OH reaction, we had to correct the raw experimental data for the following: (a) the decrease in the laser fluence along the jet due to the absorption by O-2 in the gas mixture, (b) the increase in temperature, and consequent decrease in gas density, as a result of energy released in the photochemical and chemical processes that occurred, and (c) the formation of OH(nu = 0) as a result of relaxation, particularly by O-2, of OH radicals formed in levels nu > 0. Once these corrections were made, the rate constant for reaction between OH and O(P-3) atoms showed little variation in the temperature range of 142 to 39 K and had a value of (3.5 +/- 1.0) x 10(-11) cm(3) molecule(-1) s(-1). It is recommended that this value is used in future chemical models of dense interstellar clouds.