Stimulated Raman scattering spectroscopy is a powerful technique for label-free molecular identification, but its broadband implementation is technically challenging. We introduce and experimentally demonstrate a novel approach based on photonic time stretch. The broadband femtosecond Stokes pulse, after interacting with the sample, is stretched by a telecom fiber to ≈15ns, mapping its spectrum in time. The signal is sampled through a fast analog-to-digital converter, providing single-shot spectra at 80-kHz rate. We demonstrate ≈10-5 sensitivity over ≈500cm-1 in the C-H region. Our results pave the way to high-speed broadband vibrational imaging for materials science and biophotonics.