High nonlinear fibers with low zero-dispersion wavelength (ZDW), high laser power tolerance and large band-gap are urgent for all-optical-band supercontinuum (SC) generations. Widely used chalcogenide fibers usually have a large ZDW and low laser power tolerance, and thus are not ideal for such purpose. Here, an ultra-low material ZDW chalcohalide (ChH) glass fiber with high nonlinearity as well as high laser power tolerance has been fabricated successfully via a novel peeling-off-extrusion method. The step-index fiber has double-cladding structure, the inner cladding is GeGaSe-CsI glass and the outer one is GeSbS jacket. The core glass has an ultra-low material ZDW of 3.5 mu m and large absorption edge of 2.0eV. The nonlinear refractive index is 6.67x10(-18) m(2)/W @1.55 mu m. Broadband SC generation covering 1.05-13.0 mu m is demonstrated in this novel ChH fiber. Such glass fiber with high nonlinearity, wide transparent range, low ZDW and high laser damage threshold is promising for the applications in the mid-infrared.