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Traditional optomechanical research is rarely studied in compound glass, especially chalcogenide glass. In this paper, the forward and backward Stimulated Brillouin Scattering (SBS) is demonstrated for the first time in a chalcogenide glass microsphere resonator. A high-purity chalcogenide glass microsphere with a high quality (<italic>Q</italic>) factor of 2.1 &#x00D7; 10⁷ is investigated using a 1550 nm tunable laser. In the experiment, the resulting mechanical vibration frequencies caused by forward and backward SBS are measured at 80 MHz and 7.8 GHz, respectively. The triply resonant Stimulated Brillouin scattering process greatly enhances the light&#x2013;acoustic interactions, enabling the threshold power to be 344 &#x03BC;W. The work demonstrated in the chalcogenide microresonator is important for the potential applications of chalcogenide glass, which has higher nonlinearity and low absorptions at mid-infrared band.