We will search for spin-orbit transitions of the Co3+ ions in LaCoO3. The ground state is a non-magnetic singlet, but there continues to be a debate about the nature of the lowest excited levels, which could either be from the intermediate spin (S=1) or high spin (S=2) terms. We have calculated the neutron cross section based on a recently-published model and obtained predictions of electronic transitions which should be present in the neutron spectrum. We will measure the spectrum up to 500 meV at base temperature and room temperature. If we can measure these excitations then it will provide a direct and unambiguous resolution to a 50-year old problem.