Submonolayer amounts of chloroaluminum-phthalocyanine on Cu(100) were studied with scanning tunneling spectroscopy. The molecule can be prepared in a fourfold symmetric state whose conductance spectrum exhibits a zero-bias feature similar to a Kondo resonance. In magnetic fields, however, this resonance splits far more than expected from the spin of a single electron. Density functional theory calculations reveal a charge transfer of 1.3 electrons to the degenerate lowest unoccupied molecular orbitals. These orbitals are mixed by the orbital momentum operator L[over ^]_{z} with a large matrix element corresponding to m_{L}≈2.7. Dehydrogenation of a ligand lifts the degerenracy of the lowest unoccupied molecular orbital, reduces the splitting in magnetic fields, and induces a polarity dependence of the spectra. Using model calculations of the spin, orbital, and vibrational degrees of freedom we show that a dynamical Jahn-Teller effect reproduces the main experimental observations.