The well-known leptonic U(1) symmetry of the Standard Model (SM) of quarks and leptons is extended to include a number of new fermions and scalars. The resulting theory has an invisible QCD axion (thereby solving the strong CP problem), a candidate for weak-scale dark matter (DM), as well as radiative neutrino masses. A possible key connection is a color-triplet scalar, which may be produced and detected at the Large Hadron Collider.