The reactions of atomic chlorine with O2 and CH4 are very important in stratospheric ozone photochemistry. The relative rates of these reactions strongly influence the ClO/HCl ratio. However, there remains considerable uncertainty in the absolute rate constants for the two reactions at stratospheric temperatures. Since only the relative rate is of primary importance in the stratosphere, experiments on the competitive chlorination of O3/CH4 mixtures have been carried out at 197--217 K, with the objective of directly measuring the rate constant ratio in this temperature range. The results show that the absolute rate constants recommended by the NASA Panel for Data evaluation (DeMore et al., 1990) are accurate on a relative basis to within 15% at stratospheric temperatures. The following rate constant upper limits are also established for temperatures near 200 K: ClO+CH3O2 → ClOO+CH3O, k<4¿10-12; ClO+CH3O2 → OClO+CH3O, k<1¿10-15 cm3 molec-1 s-1. ¿ American Geophysical Union 1991