We present the results of a search for pair production of the supersymmetric partner of the top quark (the top squark t1) decaying to a b quark and a chargino χ±1 with a subsequent χ±1 decay into a neutralino χ01, lepton ℓ, and neutrino ν. Using a data sample corresponding to 2.7  fb−1 of integrated luminosity of pp collisions at s√=1.96  TeV collected by the CDF II detector, we reconstruct the mass of top squark candidate events and fit the observed mass spectrum to a combination of standard model processes and t1t1 signal. We find no evidence for t1t1 production and set 95% C.L. limits on the masses of the top squark and the neutralino for several values of the chargino mass and the branching ratio B(χ±1→χ01ℓ±ν).