We demonstrate that broadband coherent anti-Stokes Raman scattering (CARS) microscopy can be very useful for fast acquisition of quantitative chemical images of multilayer polymer blends. Since a raw CARS signal results from coherent interference of resonant Raman and nonresonant background, its intensity is not linearly proportional to the concentration of molecules of interest, and it is challenging to perform a quantitative image analysis of a CARS image. Here we have developed a sequence of data processing steps to retrieve background-free and noise-reduced Raman spectra over the whole frequency range including both the fingerprint and C-H regions. Using a classical least squares approach, we are able to decompose a Raman hyperspectral image of a tertiary polymer blend into quantitative chemical images of individual components. We use this method to acquired 3-D sectioned quantitative chemical images of a multilayer polymer blend of polystyrene/styrene-ethylene-propylene-copolymer/polypropylene.