We describe a stimulated Brillouin gain (SBG) spectrometer based on low power continuous‐wave frequency‐stabilized lasers. The high resolution and broad tuning range of this spectrometer are demonstrated through a SBG spectrum of glycerol in the glassy state (T=146 K). The narrow Brillouin linewidth (17 MHz half‐width at half‐maximum) and large Brillouin shift (17.31 GHz) in this spectrum illustrate the extremely high equivalent ‘‘finesse’’ of the instrument, a finesse that would be difficult to achieve through interferometric techniques. The accuracy and precision with which the Brillouin shift can be measured are demonstrated using SBG spectra of liquid methylene chloride as an example. Our Brillouin shift values obtained over the temperature range 178–300 K are in excellent agreement with values measured previously by others using spontaneous and stimulated Brillouin scattering.