We propose and investigate theoretically the Kerr squeezing of light at a wavelength of 2 µm in chalcogenide fibers with large nonlinearity and-this is the advance-with much reduced attenuation. We present suitably realistic but straightforward designs of low-loss step-index single-mode fibers with the nonlinear Kerr coefficient 3 to 4 orders of magnitude higher than for standard telecommunication fibers, and we give estimations of optimal squeezing for continuous wave laser signal in the considered fibers based on As2S3 or As2Se3 glasses.