We present a Fourier-transform coherent anti-Stokes Raman scattering (FT-CARS) spectroscopy technique that achieves broadband CARS measurements at an ultrahigh scan rate of more than 20,000 spectra/s - more than 20 times higher than that of previous broadband coherent Raman scattering spectroscopy techniques. This is made possible by an integration of a FT-CARS system and a rapid-scanning retro-reflective optical path length scanner. To demonstrate the technique's strength, we use it to perform broadband CARS spectroscopy of the transient mixing dynamics of toluene and benzene in the fingerprint region (200-1500 cm(-1)) with spectral resolution of 10 cm(-1) at a record high scan rate of 24,000 spectra/s. Our rapid-scanning FT-CARS technique holds great promise for studying chemical dynamics and wide-field label-free biomedical imaging.