Chalcogenide hollow-core anti-resonant fibers (HC-ARFs) are a promising propagation medium for high-power mid-infrared (3-5 µm) laser delivery, while their properties have not been well understood and their fabrications remain challenging. In this paper, we design a seven-hole chalcogenide HC-ARF with touching cladding capillaries, which was then fabricated from purified As40S60 glass by combining the "stack-and-draw" method with a dual gas path pressure control technique. In particular, we predict theoretically and confirm experimentally that such medium exhibits higher-order mode suppression properties and several low-loss transmission bands in the mid-infrared spectrum, with the measured fiber loss being as low as 1.29 dB/m at 4.79 µm. Our results pave the way for the fabrication and implication of various chalcogenide HC-ARFs in mid-infrared laser delivery systems.