It is shown experimentally that in the soft X-ray region a large circular dichroism in the photoelectron angular distribution (CDAD) exists for both valence orbitals and core levels of CO molecules adsorbed on Pd(111). From theoretical consideration it follows that in the case of a spherically symmetric ground state wave function, like the 1σ and 2σ orbitals of CO, CDAD appears due to the lack of spherical symmetry in the final state. For carbon K-shell experimental results are compared to model calculations. Investigations at the Pd core levels proved that CDAD does also arise in X-ray photo-emission from non-magnetic crystals.