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Up to 16-dB frequency noise reduction and a linewidth 8 times narrower than that of the pump source is reported for the Stokes component in a compact Brillouin fiber laser (BFL) made up of chalcogenide microstructured fiber. Since the pump wave is not resonant in the ring cavity, an active stabilization of the laser is not primordial, thus making the system simpler and cheaper. Although only a 3-meter-long microstructured chalcogenide fiber is used as gain medium, a very low laser threshold power of 6 mW is obtained for nonresonant pumping. The linewidth-narrowing effect achieved in our BFL cavity is also discussed.