The surface electronic states of W(110)-(1 x 1)H have been measured using spin- and angle-resolved photoemission. We directly demonstrate that the surface bands are both split and spin-polarized by the spin-orbit interaction in association with the loss of inversion symmetry near a surface. We observe 100% spin polarization of the surface states, with the spins aligned in the plane of the surface and oriented in a circular fashion relative to the Smacr; symmetry point. In contrast, no measurable polarization of nearby bulk states is observed.