By using density functional theory, we have studied the atomic and electronic structures of Lanthanum on the chain-like reconstructed Si(111)-(2 x 3) surface with and without spin orbit coupling effect. The Lanthanum atoms are located between the pi-bonded Seiwatz Si-chains at the vicinal region on the surface. The calculated electronic band structure is semiconductor in character and the band gap is calculated value of 0.74 eV. The most of the surface states are related to stabilization of Si dangling bonds by Lanthanum atoms. When including the spin-orbit coupling effect, there is only relatively small splitting in the highest occupied state which is amount of 10.8 meV along the high symmetry points.