There exists one experimental result that cannot be explained by the Standard Model (SM), the current theoretical framework for particle physics: non-zero masses for the neutrinos (elementary particles travelling close to light speed, electrically neutral and weakly interacting). The SM assumes that they are massless. Therefore, particle physicists are now exploring new physics beyond the SM. There is strong anticipation that we are about to unravel it, in the form of new matter and/or forces, at the Large Hadron Collider (LHC), presently running at CERN. We discuss a minimal extension of the SM, based on a somewhat larger version of its symmetry structure and particle content, that can naturally explain the existence of neutrino masses while also predicting novel signals accessible at the LHC, including a light Higgs boson, as evidenced by current data.