Using data corresponding to 6.0  fb−1 of pp collisions at s√=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 in the central region with 10 GeV or more of transverse energy ttγ. The events are selected by looking for a lepton (ℓ or μ), a photon (γ), significant transverse momentum imbalance (E̸T), large total transverse energy, and three or more jets, with at least one identified as containing a b quark (b). Using an event selection optimized for the ttγ candidate sample, we also measure the cross section of tt (σtt). We measure the ttγ cross section (σttγ) to be 0.18±0.08  pb, and the ratio of σttγ to σtt to be 0.024±0.009. We observe a probability of 0.0015 (3.0 standard deviations) of the background (non-ttγ events alone producing 30 events or more.