We present a study of eeγ and μμγ events using 1109 (1009) pb−1 of data in the electron (muon) channel, respectively. These data were collected with the DØ detector at the Fermilab Tevatron collider at . Having observed 453 (515) candidates in the eeγ (μμγ) final state, we measure the Zγ production cross section for a photon with transverse energy ET>7 GeV, separation between the photon and leptons ΔRℓγ>0.7, and invariant mass of the di-lepton pair Mℓℓ>30 GeV/c2, to be 4.96±0.30(stat.+syst.)±0.30(lumi.) pb, in agreement with the Standard Model prediction of 4.74±0.22 pb. This is the most precise Zγ cross section measurement at a hadron collider. We set limits on anomalous trilinear Zγγ and ZZγ gauge boson couplings of , and , at the 95% C.L. for the form-factor scale Λ=1.2 TeV.