Advances in optical spectroscopy and microscopy have had a profound impact throughout the physical, chemical and biological sciences. One example is coherent Raman spectroscopy, a versatile technique interrogating vibrational transitions in molecules. It offers high spatial resolution and three-dimensional sectioning capabilities that make it a label-free tool for the non-destructive and chemically selective probing of complex systems. Indeed, single-colour Raman bands have been imaged in biological tissue at video rates by using ultra-short-pulse lasers. However, identifying multiple, and possibly unknown, molecules requires broad spectral bandwidth and high resolution. Moderate spectral spans combined with high-speed acquisition are now within reach using multichannel detection or frequency-swept laser beams. Laser frequency combs are finding increasing use for broadband molecular linear absorption spectroscopy. Here we show, by exploring their potential for nonlinear spectroscopy, that they can be harnessed for coherent anti-Stokes Raman spectroscopy and spectro-imaging. The method uses two combs and can simultaneously measure, on the microsecond timescale, all spectral elements over a wide bandwidth and with high resolution on a single photodetector. Although the overall measurement time in our proof-of-principle experiments is limited by the waiting times between successive spectral acquisitions, this limitation can be overcome with further system development. We therefore expect that our approach of using laser frequency combs will not only enable new applications for nonlinear microscopy but also benefit other nonlinear spectroscopic techniques.