This article presents a measurement of the top quark mass using the CDF II detector at Fermilab. Colliding beams of protons and antiprotons at Fermilab's Tevatron (root s=1.96 TeV) produce top/antitop pairs, which decay to W(+)W(-)b (b) over bar; events are selected where one W decays to hadrons and the other W decays to either e or mu plus a neutrino. The data sample corresponds to an integrated luminosity of approximately 318 pb(-1). A total of 165 u (u) over bar events are separated into four subsamples based on jet transverse energy thresholds and the number of b jets identified by reconstructing a displaced vertex. In each event, the reconstructed top quark invariant mass is determined by minimizing a chi(2) for the overconstrained kinematic system. At the same time, the mass of the hadronically decaying W boson is measured in the same event sample. The observed W boson mass provides an in situ improvement in the determination of the hadronic jet energy scale. A simultaneous likelihood fit of the reconstructed top quark masses and the W boson invariant masses in the data sample to distributions from simulated signal and background events gives a top quark mass of 173.5(-3.8)(+3.9) GeV/c(2). RI Lancaster, Mark/C-1693-2008; Levy, Stephen/C-3493-2011; Ruiz, Alberto/E-4473-2011; Robson, Aidan/G-1087-2011; Prokoshin, Fedor/E-2795-2012; Azzi, Patrizia/H-5404-2012