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Propagation dynamics of the cosh-Airy vortex (CAiV) beams in a chiral medium is investigated analytically with Huygens-Fresnel diffraction integral formula. The results show that the CAiV beams are split into the left circularly polar-ized vortex (LCPV) beams and the right circularly polarized vortex (RCPV) beams with different propagation trajectories in the chiral medium. We mainly investigate the effect of the cosh parameter on the propagation process of the CAiV beams. The propagation characteristics, including intensity distribution, propagation trajectory, peak intensity, main lobe’s inten-sity, Poynting vector, and angular momentum are discussed in detail. We find that the cosh parameter affects the intensity distribution of the CAiV beams but not its propagation trajectory. As the cosh parameter increases, the distribution areas of the LCPV and RCPV beams become wider, and the side lobe’s intensity and peak intensity become larger. Besides, the main lobe’s intensity of the LCPV and RCPV beams increase with the increase of the cosh parameter at a farther prop-agation distance, which is confirmed by the variation trend of the Poynting vector. It is significant that we can vary the cosh parameter to control the intensity distribution, main lobe’s intensity, and peak intensity of the CAiV beams without changing the propagation trajectory. Our results may provide some support for applications of the CAiV beams in optical micromanipulation.