  We report a measurement of the top quark mass using events collected by the
CDF II Detector from ppbar collisions at \sqrt{s} = 1.96 TeV at the Fermilab
Tevatron. We calculate a likelihood function for the top mass in events that
are consistent with ttbar->bbar l^- \nubar b l^+ \nu decays. The likelihood is
formed as the convolution of the leading-order matrix element and detector
resolution functions. The joint likelihood is the product of likelihoods for
each of 33 events collected in 340 pb^{-1} of integrated luminosity, yielding a
top quark mass M_t = 165.2 +- 6.1 (stat.) +- 3.4(syst.) GeV/c^2. This first
application of a matrix-element technique to ttbar->bbar l^- \nubar b l^+ \nu
decays gives the most precise single measurement of M_t in dilepton events.
Combined with other CDF Run II measurements using dilepton events, we measure
M_{t} = 167.9 +- 5.2 (stat.) +- 3.7 (syst.) GeV/c^2.
