The new oxyselenide La2Co2Se2O3, containing Co2O square-planar layers, has been successfully synthesized using solid-state reactions under vacuum. The compound crystallizes in space group 14/mmm with lattice parameters a=4.0697(8) angstrom and c=18.419(4) angstrom. Magnetic susceptibility measurements indicate an antiferromagnetic transition at similar to 220 K. The magnetic entropy associated with the transition is close to R In 2, suggesting an unusual low-spin state for the Co2+ ions. The as-prepared sample shows insulating behavior with room-temperature resistivity of similar to 10(7) Omega cm, which decreases by 4 orders of magnitude under a pressure of 7 GPa. Band structure calculations using the LSDA+U approach reproduce the insulating ground state with low spin for Co and suggest strong orbital polarization for the valence electrons near the Fermi level. It is also revealed that the spin and orbital degrees of freedom in the antiferromagnetic checkerboard spin-lattice are mutually coupled.