We present the first demonstration, to our knowledge, of a label-free flow cytometer for the analysis of biological specimens using multiplex coherent anti-Stokes Raman scattering (MCARS) and elastic scatter measurements. The MCARS system probes the Raman vibrational energy levels and the elastic scatter provides morphological information. We demonstrate these capabilities by probing a culture of Saccharomyces cerevisiae at 100 spectra/s and constructing a background-free Raman reconstruction using a Kramers-Kronig relation. A theoretical analysis shows that this system could operate at speeds of 10 kHz with appropriate hardware; thus facilitating integration into commercial flow cytometers or use as a high-speed, stand-alone device.