The new oxyselenide La(2)Co(2)Se(2)O(3), containing Co(2)O square-planar layers, has been successfully synthesized using solid-state reactions under vacuum. The compound crystallizes in space group I4/mmm with lattice parameters a = 4.0697(8) A and c = 18.419(4) A. Magnetic susceptibility measurements indicate an antiferromagnetic transition at approximately 220 K. The magnetic entropy associated with the transition is close to R ln 2, suggesting an unusual low-spin state for the Co(2+) ions. The as-prepared sample shows insulating behavior with room-temperature resistivity of approximately 10(7) ohms 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.