A search is performed for top-quark pairs (t (t) over bar) produced together with a photon (gamma) with transverse energy greater than 20 GeV using a sample of t (t) over bar candidate events in final states with jets, missing transverse momentum, and one isolated electron or muon. The data set used corresponds to an integrated luminosity of 4.59 fb(-1) of proton-proton collisions at a center-of-mass energy of 7 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. In total, 140 and 222 t (t) over bar gamma candidate events are observed in the electron and muon channels, to be compared to the expectation of 79 +/- 26 and 120 +/- 39 non-t (t) over bar gamma background events, respectively. The production of t (t) over bar gamma events is observed with a significance of 5.3 standard deviations away from the null hypothesis. The t (t) over bar gamma production cross section times the branching ratio (BR) of the single-lepton decay channel is measured in a fiducial kinematic region within the ATLAS acceptance. The measured value is sigma(fid)(t (t) over bar gamma) x BR = 63 +/- 8(stat)(-13)(+17) (syst) +/- 1(lumi) fb per lepton flavor, in good agreement with the leading-order theoretical calculation normalized to the next-to-leading-order theoretical prediction of 48 +/- 10 fb.