We introduce a single-shot interferometric approach to suppress the nonresonant background (NRB) contribution to a broadband coherent anti-Stokes Raman scattering (CARS) spectrum; this single-shot approach is conducive to rapid imaging. A pulse shaper prepares a narrowband pulse with two spectral components of differing phase. When the CARS fields generated by these two out-of-phase components are optically mixed, NRB signal is greatly reduced while a resonant CARS signal remains with minimal attenuation. We discuss and demonstrate two model schemes for the interfering pulse components: (1) two pulses with different bandwidths and the same center frequency (ps-fs scheme) and (2) two pulses with the same bandwidth and shifted center frequencies (ps-ps scheme). In both schemes, only the resonant signal from the "3-color" CARS mechanism survives. The resonant signal from "2-color" CARS mechanism vanishes along with the NRB. We discuss optimization conditions for signal intensity and shape of resonant CARS peaks. Experimental CARS spectra of c-hexane and benzonitrile demonstrate feasibility of these approaches.