Strong spin-orbit coupling lifts the degeneracy of t 2g orbitals in 5d transition-metal systems, leaving a Kramers doublet and quartet with effective angular momentum of J eff = 1/2 and 3/2, respectively. These spin-orbit entangled states can host exotic quantum phases such as topological Mott state, unconventional superconductivity, and quantum spin liquid. The lacunar spinel GaTa4Se8 was theoretically predicted to form the molecular J eff = 3/2 ground state. Experimental verification of its existence is an important first step to exploring the consequences of the J eff = 3/2 state. Here, we report direct experimental evidence of the J eff = 3/2 state in GaTa4Se8 by means of excitation spectra of resonant inelastic X-ray scattering at the Ta L3 and L2 edges. We find that the excitations involving the J eff = 1/2 molecular orbital are absent only at the Ta L2 edge, manifesting the realization of the molecular J eff = 3/2 ground state in GaTa4Se8.The strong interaction between electron spin and orbital degrees of freedom in 5d oxides can lead to exotic electronic ground states. Here the authors use resonant inelastic X-ray scattering to demonstrate that the theoretically proposed J eff = 3/2 state is realised in GaTa4Se8.