Due to its high molecular specificity, Raman spectroscopy is a well-established analytical tool. Usually the inelastically scattered Raman light is spectrally dispersed by a spectrometer. Here, we present an alternative method, using an optical fiber as dispersive element. As the group velocity within the fiber is wavelength-dependent, different Raman bands arrive at different times at the detector. In combination with timecorrelated single-photon counting, Raman spectra can be measured in the time domain. As detector we implemented a Superconducting Nanowire Single-Photon Detector (SNSPD), which possesses an unrivaled timing accuracy of about 20 ps. Within this contribution we show first results of Raman spectra measured in the time domain using gradient index fibers of varying length.