In this paper, we report the design and fabrication of a highly birefringent polarization-maintaining photonic crystal fiber (PM-PCF) made from chalcogenide glass, and its application to linearly-polarized supercontinuum (SC) generation in the mid-infrared region. The PM fiber was drawn using the casting method from As38Se62 glass which features a transmission window from 2 to 10 $mu m$ and a high nonlinear index of 1.13.10$^{-17}$m$^{2}$W$^{-1}$. It has a zero-dispersion wavelength around 4.5 $mu m$ and, at this wavelength, a large birefringence of 6.10$^{-4}$ and consequently strong polarization maintaining properties are expected. Using this fiber, we experimentally demonstrate supercontinuum generation spanning from 3.1-6.02 $mu m$ and 3.33-5.78 $mu m$ using femtosecond pumping at 4 $mu m$ and 4.53 $mu m$, respectively. We further investigate the supercontinuum bandwidth versus the input pump polarization angle and we show very good agreement with numerical simulations of the two-polarization model based on two coupled generalized nonlinear Schrodinger equations.