The reflection and transmission properties of plane waves on the interface of uniaxial chiral media with the optical axis parallel to the interface are investigated. The formulas of the reflected and transmitted power are derived. The curves of the group refractive angles, power of the reflected and transmitted waves for TE and TM incident waves are presented for three cases of dielectric constant combinations and for non-chiral, weak chiral and strong chiral media. Some new results are obtained, which are different from those in the uniaxial chiral media with the optical axis perpendicular to the interface.