The propagation properties of Hermite-cosine-hyperbolic-Gaussian beam (HChGB) in a chiral medium are investigated. Analytical formula for a HChGB beam propagating through a chiral medium is derived theoretically based on the Huygens-Fresnel Integral, and the propagation properties are illustrated numerically and discussed. Results show that the evolution properties of the HChGB in a chiral medium are closely related to the beam order, the chirality factor and the decentered parameter b.