High-purity Ge-As-Se and Ge-As-S chalcogenide glasses were prepared by modified physical and chemical purification techniques. Using the purified glasses, step-index fibers with a small core (similar to 5.5 mu m) and large numerical aperture (similar to 1.3) were fabricated. When a 13.5-cm-long fiber was pumped with 320 fs pulses at a repetition rate of 10.5 MHz at 4.1 mu m, supercontinuum spanning from similar to 1.8 to similar to 9.8 mu m with a dynamic range of similar to 10 dB and an average power of similar to 3 mW was generated.