We report the fabrication of a chalcogenide all-solid hybrid microstructured optical fiber and its application in supercontinuum generation for the first time, to the best of our knowledge. The fiber possesses all-normal and flattened chromatic dispersion, making it highly potential for broad and coherent supercontinuum generation. By pumping the fiber with a femtosecond laser at 3, 4, and 5 μm, broad supercontinua with good spectral flatness are generated. The broadest SC spectrum extending from 2.2 to 10 μm at -20 dB level was obtained when the fiber was pumped at 5 μm with an input power of 3.9 mW.