We report on measurements of the nonlinear index of refraction of air, N2, and O2 at a wavelength close to 10 μm by collinear four-wave mixing of a 200 MW CO2 laser beat-wave. The use of a 200 ps long beat-wave comprising radiation amplified on the 10P20 and 10R16 lines of the CO2 laser provides a sensitive method to measure the small nonlinearities characteristic of the gas phase in a spectral region where no such data exists.