Multiple reflection of light at the interface of an isotropic chiral medium (either transparent or absorbing) and a transparent achiral dielectric is studied as a function of angle of incidence and number of reflections to ascertain whether there is an enhancement (with respect to single-pass reflection) of (i) the difference in reflected left and right circularly polarized waves, and (ii) the ellipticity of reflected linearly polarized waves. It is shown that for ordinary reflection, where the mean refractive index n of the chiral medium is greate than the refractive index no of the incident medium, multiple reflection does not lead to a significant enhancement. However, in the vicinity of total reflection (no> n) the chiral asymmetries resulting from N reflections are significantly greater than those for one reflection; at critical angle the enhancement is approximately by a factor N.