We present a measurement of the mass of the top quark from p anti-p
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
p anti-p --> tt-bar 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
tt-bar 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.