We present the results of a search for pair production of a new heavy toplike quark t′ decaying to a W boson and another quark using the Collider Detector at Fermilab II detector in run II of the Tevatron pp collider. Using a data sample corresponding to 760  pb−1 of integrated luminosity, we fit the observed spectrum of total transverse energy and reconstructed t′ quark mass to a combination of standard model processes and t′ pair production. We see no evidence for t′t′ production, and we infer a lower limit of 256  GeV/c2 on the mass of the t′ at 95% C.L. assuming standard strong couplings for the t′.