This paper proposes a design and mathematical study of As2S3 chalcogenide photonic crystal fiber (PCF) for broadband supercontinuum generation. The proposed design offers a large nonlinearity coefficient and ultra-flattened dispersion. The proposed design was analyzed using the full-vectorial finite element method. Through this method, it is shown that an ultra-broad supercontinuum spectrum of 0.8-4.5 μm is attained using an As2S3 core PCF design with 20 fs pump pulse width and a length of 10 mm, having 3 kW power at a -40 dB spectral and temporal intensity. The proposed octagonal PCF has shown a low zero dispersion wavelength at the pump wavelength of 1.55 μm.