We investigate the refraction and propagation properties of electromagnetic waves which are incident from free space to a biaxially anisotropic chiral medium. Such a chiral medium can be realized by putting chiral elements pointing to two directions into a host medium. When the host medium is a normally isotropic dielectric, no negative refraction and/or backward waves are supported for the propagating eigenwaves in the chiral medium. When the host medium changes to an anisotropic dielectric or an electric plasma, however, negative refractions and backward waves can be realized separately or even simultaneously if we choose the medium parameters properly. Numerical simulations validate our theoretical analysis.