We present the first observation of the Zγ→νν¯γ process at the Fermilab Tevatron at 5.1 standard deviations significance, based on 3.6 fb−1 of integrated luminosity collected with the D0 detector at the Fermilab Tevatron pp¯ Collider at s=1.96 TeV. The measured Zγ production cross section multiplied by the branching fraction of Z→νν¯ is 32±9(stat+syst)±2(lumi) fb for the photon ET>90 GeV. It is in agreement with the standard model prediction of 39±4 fb. We set limits on anomalous trilinear Zγγ and ZZγ gauge boson couplings, most of which are the most restrictive to date.Received 12 February 2009DOI:https://doi.org/10.1103/PhysRevLett.102.201802©2009 American Physical Society