The magnetic ground state and the crystalline electric field level scheme of the triangular lattice antiferromagnet KCeO2 are investigated. Below TN=300 mK, KCeO2 develops signatures of magnetic order in specific heat measurements and low energy inelastic neutron scattering data. Trivalent Ce3+ ions in the D3d local environment of this compound exhibit large splittings among the lowest three 4f1 Kramers doublets defining for the free ion the J=5/2 sextet and a ground state doublet with dipole character, consistent with recent theoretical predictions in M. S. Eldeeb et al. Phys. Rev. Materials 4, 124001 (2020). An unexplained, additional local mode appears, and potential origins of this anomalous mode are discussed.