Using data corresponding to 6.0fb-1 of pp̄ collisions at √s=1.96TeV 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 tt̄γ. The events are selected by looking for a lepton (ℓ or μ), a photon (γ), significant transverse momentum imbalance (ET), 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 tt̄γ candidate sample, we also measure the cross section of tt̄ (σtt̄). We measure the tt̄γ cross section (σtt̄γ) to be 0.18±0.08pb, and the ratio of σtt̄γ to σtt̄ to be 0.024±0.009. We observe a probability of 0.0015 (3.0 standard deviations) of the background (non-tt̄γ events alone producing 30 events or more. © 2011 American Physical Society.