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The first observation of electroweak production of a photon in association with two forward jets in proton-proton collisions is presented. The measurement uses data recorded by the CMS experiment at the LHC during 2016–2018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb−1. The analysis is performed in a region enriched in photon production via vector boson fusion, with a requirement on the transverse momentum of the photon to exceed 200 GeV. The cross section is measured to be 202−32+36 fb, at a significance with respect to the null hypothesis that exceeds five standard deviations. This is in agreement with the standard model prediction of 177−12+13 fb. Differential cross sections are measured as a function of various observables. Limits are set on dimension-6 effective field theory operators that contribute to the WWγ interaction. The observed 95% confidence intervals for the corresponding Warsaw basis Wilson coefficients cW and cHWB are [−0.11, 0.16] and [−1.6, 1.5], respectively.