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We demonstrate the generation of a low-noise, octave-spanning mid-infrared supercontinuum from 1700 to 4800 nm by injecting femtosecond pulses into the normal dispersion regime of a multimode step-index chalcogenide fiber with 100 µm core diameter. We conduct a systematic study of the intensity noise across the supercontinuum spectrum and show that the initial fluctuations of the pump laser are at most amplified by a factor of three. We also perform a comparison with the noise characteristics of an octave-spanning supercontinuum generated in the anomalous dispersion regime of a multimode fluoride fiber with similar core size and show that the normal dispersion supercontinuum in the multimode chalcogenide fiber has superior noise characteristics. Our results open up novel perspectives for many practical applications such as long-distance remote sensing where high power and low noise are paramount.