A discharge flow system with laser magnetic resonance (LMR), resonance fluorescence (RF), and resonance absorption (RA) detection axes is used to study the kinetics of the title reaction. Pseudo-first-order decays of O in excess ClO and of ClO in excess O agree very well and yield a rate constant of (3.5¿0.5)¿10-11 cm3 molecule-1 s-1 near 300 K, with no discernable temperature dependence over the range 252-347 K. Both reactants, and for some experiments the Cl atom product, are detected directly with high sensitivity. Experiments are done both in helium and in argon, and the cited uncertainties include an estimate of systematic errors at the 2&sgr; or 95% confidence level. Results are compared with other recent work, and implications of the somewhate slower rate constant on the chlorine-induced destruction of O3 in the stratosphere are considered.