Coherent Anti-Stokes Raman Scattering (CARS) processes are ``coherent,'' but the phase of the anti-Stokes radiation is usually lost by most incoherent spectroscopic CARS measurements. We propose a novel Raman microscopy imaging method called Nonlinear Interferometric Vibrational Imaging, which measures Raman spectra by obtaining the temporal anti-Stokes signal through nonlinear interferometry. With a more complete knowledge of the anti-Stokes signal, we show through simulations that a high-resolution Raman spectrum can be obtained of a molecule in a single pulse using broadband radiation. This could be useful for identifying the three-dimensional spatial distribution of molecular species in tissue.