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 (s√=1.96  TeV) produce top/antitop pairs, which decay to W+W−bb; events are selected where one W decays to hadrons and the other W decays to either e or μ plus a neutrino. The data sample corresponds to an integrated luminosity of approximately 318  pb−1. A total of 165 tt 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 χ2 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+3.9−3.8  GeV/c2.