Flow cytometry is an indispensable tool in biology for counting and analyzing single cells in large heterogeneous populations. However, it predominantly relies on fluorescent labeling to differentiate cells and, hence, comes with several fundamental drawbacks. Here, we present a high-throughput Raman flow cytometer on a microfluidic chip that chemically probes single live cells in a label-free manner. It is based on a rapid-scan Fourier-transform coherent anti-Stokes Raman scattering spectrometer as an optical interrogator, enabling us to obtain the broadband molecular vibrational spectrum of every single cell in the fingerprint region (400 to 1600 cm-1) with a record-high throughput of ~2000 events/s. As a practical application of the method not feasible with conventional flow cytometry, we demonstrate high-throughput label-free single-cell analysis of the astaxanthin productivity and photosynthetic dynamics of Haematococcus lacustris.