The spin Hall effect (SHE) of light beams reflected from an air-chiral interface are investigated systematically. Due to the intrinsic chiral asymmetry of the medium, a horizontally polarized incident Gaussian beam will undergo asymmetric spin splitting, i.e., both the displacements and energies of two spin components of the reflected beam are different. One spin component can undergo large displacement near points of |rpp| = |rsp| (rpp and rsp are the Fresnel reflection coefficients), where the reflected beams are almost in circular polarization states. Moreover, for an incident beam carrying orbital angular momentum (OAM), the two spin components acquire additional OAM dependent shifts, which attribute to the asymmetric spin splitting. Thus, the asymmetric spin splitting of the reflected beam will vary with the incident OAM. These findings provide a deeper insight into the SHE of light, and they may have potential application in precision metrology.