We report on a giant Rashba type splitting of metallic bands observed in one-dimensional structures prepared on a vicinal silicon substrate. A single layer of Pb on Si(553) orders this vicinal surface making perfectly regular distribution of monatomic steps. Although there is only one layer of Pb, the system reveals very strong metallic and purely one-dimensional character, which manifests itself in multiple surface state bands crossing the Fermi level in the direction parallel to the step edges and a small band gap in the perpendicular direction. As shown by spin-polarized photoemission and density functional theory calculations these surface state bands are spin-polarized and completely decoupled from the rest of the system. The experimentally observed spin splitting of 0.6 eV at room temperature is the largest found to now in the silicon-based metallic nanostructures, which makes the considered system a promising candidate for application in spintronic devices.