We present a measurement of the mass of the top quark from proton-antiproton collisions recorded at the CDF experiment in Run II of the Fermilab Tevatron. We analyze events from the single lepton plus jets final state (tt→W+bW−b→lνbqq′b). The top-quark mass is extracted using a direct calculation of the probability density that each event corresponds to the tt final state. The probability is a function of both the mass of the top quark and the energy scale of the calorimeter jets, which is constrained in situ by the hadronic W boson mass. Using 167 events observed in 955  pb−1 of integrated luminosity, we achieve the single most precise measurement of the top-quark mass, 170.8±2.2(stat.)±1.4(syst.)  GeV/c2.