A precision measurement of the top quark mass mt is obtained using a sample of tt events from pp collisions at the Fermilab Tevatron with the CDF II detector. Selected events require an electron or muon, large missing transverse energy, and exactly four high-energy jets, at least one of which is tagged as coming from a b quark. A likelihood is calculated using a matrix element method with quasi-Monte Carlo integration taking into account finite detector resolution and jet mass effects. The event likelihood is a function of mt and a parameter ΔJES used to calibrate the jet energy scale in situ. Using a total of 1087 events in 5.6  fb−1 of integrated luminosity, a value of mt=173.0±1.2  GeV/c2 is measured.