We report coherent anti-Stokes Raman scattering correlation spectroscopy (CARS-CS) that measures the fluctuation of the CARS signal from scatterers in a subfemtoliter excitation volume. This method probes dynamical processes with chemical selectivity based on vibration spectroscopy. High-sensitivity CARS-CS measurements are carried out with epi-detection or polarization-sensitive detection. Theoretical expressions of CARS intensity autocorrelation functions are derived and supported by experimental data. The properties of CARS-CS are-characterized with measurements of diffusion dynamics of small polystyrene spheres.