Transition metal compounds sometimes exhibit attractive colors. Here, we report a new oxychloride, Ca3ReO5Cl2, that shows unusually distinct pleochroism; that is, the material exhibits different colors depending on the viewing direction. This pleochroism is a consequence of the coincidental complex crystal field splitting of the 5d orbitals of the Re6+ ion in a square-pyramidal coordination of low symmetry in the energy range of the visible spectrum. Since the relevant d-d transitions show characteristic polarization dependence according to the optical selection rule, the orbital states are "visible" in Ca3ReO5Cl2.