We present X-ray photoelectron, Co L2,3 and O K X-ray absorption, as well as Co Kβ1,3 X-ray emission spectroscopy results of studies of the spin states of trivalent cobalt ions in single-crystal cobaltite LaCoO3. We show that at room temperature, in the bulk of a LaCoO3 single crystal, Co3+ ions are in the low-spin state, while high-spin Co2+, high-spin Co3+, low-spin Co3+ , and probably also intermediate-spin Co3+ ions are localated on the surface.