  In a search for new phenomena in a signature suppressed in the standard model
of elementary particles (SM), we compare the inclusive production of events
containing a lepton, a photon, significant transverse momentum imbalance (MET),
and a jet identified as containing a b-quark, to SM predictions. The search
uses data produced in proton-antiproton collisions at 1.96 TeV corresponding to
1.9 fb-1 of integrated luminosity taken with the CDF detector at the Fermilab
Tevatron. We find 28 lepton+photon+MET+b events versus an expectation of
31.0+4.1/-3.5 events. If we further require events to contain at least three
jets and large total transverse energy, simulations predict that the largest SM
source is top-quark pair production with an additional radiated photon,
ttbar+photon. In the data we observe 16 ttbar+photon candidate events versus an
expectation from SM sources of 11.2+2.3/-2.1. Assuming the difference between
the observed number and the predicted non-top-quark total is due to SM top
quark production, we estimate the ttg cross section to be 0.15 +- 0.08 pb.
