We compare the inclusive production of events containing a lepton (ℓ), a photon (γ), significant transverse momentum imbalance (E̸T), and a jet identified as containing a b-quark, to SM predictions. The search uses data produced in proton-antiproton collisions at s√=1.96  TeV corresponding to 1.9  fb−1 of integrated luminosity taken with the CDF detector. We find 28 ℓγbE̸T 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, the largest SM source is radiative top-quark pair production, tt+γ. In the data we observe 16 ttγ 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 of 6.8+2.2−2.0 is due to SM top-quark production, we estimate the ttγ cross section to be 0.15±0.08  pb.