  A search is presented for the standard model Higgs boson produced in
association with top quarks using the full Run II proton-antiproton collision
data set, corresponding to 9.45 inverse fb, collected by the Collider Detector
at Fermilab. No significant excess over the expected background is observed,
and 95% credibility-level upper bounds are placed on the cross section
sigma(t\bar{t}H --> lepton + missing transverse energy + jets). For a Higgs
boson mass of 125 GeV, we expect to set a limit of 12.6, and observe a limit of
20.5 times the standard model rate. This represents the most sensitive search
for a standard model Higgs boson in this channel to date.
