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Based on a general beam-propagation model, we derive in the paraxial approximation the analytical expressions for the spatial transverse shift (TS) and the angular TS of a beam reflected from the air-chiral interface. The results show that the TSs are closely related to the propagation behaviors of the right-circularly polarized (RCP) and the left-circularly polarized (LCP) waves in the chiral medium. When the L(R)CP wave becomes evanescent, the left (right)-elliptically polarized incident beam suffers a smaller TS. When the L(R)CP wave propagates, the left (right)-elliptically polarized incident beam experiences a greater TS. When the total internal reflection happens, neither of the two elliptically polarized incident beams suffers TSs. TSs can be controlled not only by adjusting the central angle of incidence, but also by tailoring the permittivity, permeability, and chirality parameter of the chiral medium. [ABSTRACT FROM AUTHOR]