This paper describes the phenomena that occur when a Gaussian beam is reflected from a dielectric-chiral interface. These phenomena include an angular shift of the peak of the reflected fields in the far field and, near the critical angle or angles, a lateral shift of the fields in the plane of the interface, known as the Goos- Hänchen shift. The waist size of the reflected fields is also found to differ from that of the incident beam, and an apparent propagation distance known as the "focal shift" also arises. The spectral domain solution of the problem is described, and approximate formulas for determining the parameters for the reflected fields are derived. The problem is also solved numerically for three specific cases of interest and the results are compared to those predicted by the approximate formulas. Lateral, angular, and focal shifts are observed for both components of the reflected field near the critical angles for the interface. It is shown that both positive and negative lateral shifts occur when beams are reflected at the dielectric-chiral interface, whereas only negative shifts are observed for the dielectric-dielectric interface. These shifts are found to occur even when the dielectric constant of the chiral region is larger than that of the pure dielectric region, if a sufficient amount of chirality exists. In all cases well known results for the dielectric-dielectric interface are recovered by setting the chirality of the second medium to zero.