The rate constant for the CH3 + C2H6 -> CH4 + C2H5 reaction was studied behind reflected shock waves at temperatures between 1369 and 1626 K and pressures from 8.6 to 47.4 atm in mixtures of methane, ethane, and argon. Ethylene time histories were measured using laser absorption of radiation from a carbon dioxide gas laser near 10.532 mu m. The resulting rate constant data can be represented by the Arrhenius equation k (T) = 3.90 X 10(13) exp(-16670 cal/mol/RT) cm(3) mol(-1) s(-1). We believe this is the first study to extend experimental data for this rate constant to temperatures above 1400 K. The overall 2 sigma uncertainty of the current data is +18%/-21% resulting primarily from uncertainties associated with the influence of secondary reactions and the fitting of rapidly changing species time histories at the higher temperatures.