Ultraviolet complete Lorentz-invariant theory with superluminal signal propagation

We describe a UV complete asymptotically fragile Lorentz-invariant theory exhibiting superluminal signal propagation. Its low energy effective action contains ``wrong'' sign higher dimensional operators. Nevertheless, the theory gives rise to an S matrix, which is defined at all energies. As expected for a nonlocal theory, the corresponding scattering amplitudes are not exponentially bounded on the physical sheet, but otherwise are healthy. We study some of the physical consequences of this S matrix.