  We present a measurement of the mass of the top quark from ppbar collisions
at 1.96 TeV observed with the Collider Detector at Fermilab (CDF) at the
Fermilab Tevatron Run II. The events have the decay signature of ppbar to ttbar
in the lepton plus jets channel in which at least one jet is identified as
coming from a secondary vertex and therefore a b-hadron. The largest systematic
uncertainty, the jet energy scale (JES), is convoluted with the statistical
error using an in-situ measurement of the hadronic W boson mass. We calculate a
likelihood for each event using leading-order ttbar and W+jets cross-sections
and parameterized parton showering. The final measured top quark mass and JES
systematic is extracted from a joint likelihood of the product of individual
event likelihoods. From 118 events observed in 680 pb-1 of data, we measure a
top quark mass of 174.09 +- 2.54 (stat+JES) +- 1.35 (syst) GeV/c2.
