We report a supercontinuum spanning well over an octave of measurable bandwidth from about 1 to 3.7 μm in a 2.1 mm long As₂S₃ fiber taper using the in situ tapering method. A sub-100-fs mode-locked thulium-doped fiber laser system with ~300 pJ of pulse energy was used as the pump source. Third-harmonic generation was observed and currently limits the pump pulse energy and achievable spectral bandwidth.