The absorption and magnetic circular dichroism spectra of 1%-3% copper(II) doped into the cubic perovskite host KZnF3 are measured over the temperature range 1.8-300 K. Sharp magnetic dipole allowed transitions (2)E(g)(Gamma(8)) --> T-2(2g)(Gamma(7),Gamma(8)) are observed together with accompanying vibrational fine structure. The spectra are interpreted on the basis of a tetragonally elongated CuF64- ground state geometry which arises from strong Jahn-Teller coupling. This results in a statistical distribution of three equivalent elongations which can undergo reorientation on the electron paramagnetic resonance time scale. The Jahn-Teller coupling within the T-2(2g) multiplet is partially quenched by spin-orbit coupling and the lowest Kramers doublet Gamma(7) has an octahedral geometry, white the higher lying Gamma(8) state has a small tetragonal distortion. This system presents an excellent opportunity to study the spectroscopy of the copper(II) ion in a cubic environment.