We have studied by angle-resolved photoelectron spectroscopy (ARPES) the band structure of the ordered surface alloy obtained by the deposition of 0.33 monolayers of Pb on the Ag(111) surface. We observe several dispersing features which are well described as Pb-Ag hybrid bands by a band structure calculation performed within the generalized gradient approximation of density functional theory. We also find that a band of mixed Pb p(z) and Ag s character is split in momentum space. We interpret this splitting as the combined result of spin-orbit interaction and broken inversion symmetry at the surface.