Abstract : Using data corresponding to 6.0 fb−1 of p¯p collisions at ps = 1.96 TeV collected by the CDF II detector, we present a cross section measurement of top-quark pair production with an additional radiated photon, t¯t . The events are selected by looking for a lepton (l), a photon (gamma), significant transverse momentum imbalance (6ET ), large total transverse energy, and three or more jets, with at least one identified as containing a b quark (b). The t¯t sample requires the photon to have 10 GeV or more of transverse energy, and to be in the central region. Using an event selection optimized for the t¯t candidate sample we measure the production cross section of t¯t (t¯t), and the ratio of cross sections of the two samples. Control samples in the dilepton+photon and lepton+photon+6ET , channels are constructed to aid in decay product identification and background measurements. We observe 30 t¯t candidate events compared to the standard model expectation of 26.9 ± 3.4 events. We measure the t¯t cross section (t¯t ) to be 0.18 ± 0.08 pb, and the ratio of t¯t to t¯t to be 0.024 ± 0.009. Assuming no t¯t production, we observe a probability of 0.0015 of the background events alone producing 30 events or more, corresponding to 3.0 standard deviations.