We have applied nonlinear interferometry of coherent anti-Stokes Raman spectroscopy (CARS) to measure the nonresonant third order susceptibilities of various gases. For the experiment, we placed two gas cells serially and filled the first cell with argon as a calibration standard and the second cell with gases under test. The interference fringes of the CARS signals generated in the two gas cells were obtained by changing the thickness of the phase shifting unit which was made of BK-7 glass. The total effective nonresonant susceptibilities were determined from the measured amplitudes of the interference fringes of the CARS signals of the gases. The nonresonant susceptibilities were obtained by subtracting off resonant vibrational contributions from the total effective susceptibilities. The results of this work are compared with the published data and the overall uncertainty is estimated to be less than 5%. an 5%.