This paper reports on the fabrication and characterization of multimaterial chalcogenide fiber tapers that have high numerical apertures (NAs). We first fabricated multimaterial As(2)Se(3)-As(2)S(3) chalcogenide fiber preforms via a modified one-step coextrusion process. The preforms were drawn into multi- and single-mode fibers with high NAs (≈1.45), whose core/cladding diameters were 103/207 and 11/246 μm, respectively. The outer diameter of the fiber was tapered from a few hundred microns to approximately two microns through a self-developed automatic tapering process. Simulation results showed that the zero-dispersion wavelengths (ZDWs) of the tapers were shorter than 2 μm, indicating that the tapers can be conveniently pumped by commercial short wavelength infrared lasers. We also experimentally demonstrated the supercontinuum generation (SCG) in a 15-cm-long multimaterial As(2)Se(3)-As(2)S(3) chalcogenide taper with 1.9 μm core diameter and the ZDW was shifted to 3.3 μm. When pumping the taper with 100 fs short pulses at 3.4 µm, a 20 dB spectral of the generated supercontinuum spans from 1.5 μm to longer than 4.8 μm.