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This report describes a measurement of the top quark mass in pp̅ collisions at a center of mass energy of 1.8 TeV. The data sample was collected with the CDF detector during the 1992–1995 collider run at the Fermilab Tevatron, and corresponds to an integrated luminosity of 106 pb-1. Candidate tt̅ events in the ‘‘lepton+jets’’ decay channel provide our most precise measurement of the top quark mass. For each event a top quark mass is determined by using energy and momentum constraints on the production of the tt̅ pair and its subsequent decay. A likelihood fit to the distribution of reconstructed masses in the data sample gives a top quark mass in the lepton+jets channel of 176.1±5.1(stat) ±5.3(syst) GeV/c2. Combining this result with measurements from the ‘‘all-hadronic’’ and ‘‘dilepton’’ decay topologies yields a top quark mass of 176.1±6.6 GeV/c2.