We point out a novel, nonuniversal contribution to the dephasing rate 1͞t w ϵ g w of conduction electrons in metallic systems: scattering off nonmagnetic two-level systems ( TLSs) having almost degenerate Kondo ground states. In the regime D ren , T , T K (D ren renormalized level splitting, T K Kondo temperature), such TLSs exhibit non-Fermi-liquid physics that can cause g w , which generally decreases with decreasing T , to seemingly saturate in a limited temperature range before vanishing for T ! 0. This could explain the saturation of dephasing recently observed in gold wires [ Mohanty et al., Phys. Rev. Lett. 78, 3366 (1997)].