Ab initio quantum-chemical cluster calculations are performed for the perovskite LaCoO3. The main concern is to calculate the energy level ordering of different spin states of Co3+, which is an issue of great controversy for many years. The calculations performed for the trigonal lattice structure at T = 5 K and 300 K, with the structural data taken from experiment, display that the low-spin (LS, S = 0) ground state is separated from the first excited high-spin (HS, S = 2) state by a gap <100 meV, while the intermediate-spin (IS, S = 1) state is located at much higher energy ≈0.5 eV. We suggest that the local lattice relaxation around the Co3+ ion excited to the HS state and the spin-orbit coupling reduce the spin gap to a value ~10 meV. Coupling of the IS state to the Jahn-Teller local lattice distortion is found to be rather strong and reduces its energy position to a value of 200 ÷ 300 meV. Details of the quantum-chemical cluster calculation procedure and the obtained results are extensively discussed and compared with those reported earlier by other authors.