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We design a nonlinear air-clad chalcogenide As2S3 subwavelength diameter fiber, referred to as nanofiber or nanowire, and calculate the chromatic dispersion in it. The zero dispersion is achieved at the core size of 500 nm for this nanofiber at the telecommunication wavelength of 1.5 mum. We further present the flattening of the zero dispersion in the telecommunication window by cladding the As2S3 core with borosilicate glass, the thermal properties of which match with those of the As2S3 glass. Zero-flattened dispersion centered at 1.408 mum wavelength can be tailored for the nanofiber with this new structure when the nanofiber core diameter is 724 nm.