The first evidence for the Higgs boson decay to a Z boson and a photon is presented, with a statistical significance of 3.4 standard deviations. The result is derived from a combined analysis of the searches performed by the ATLAS and CMS Collaborations with proton-proton collision datasets collected at the CERN Large Hadron Collider (LHC) from 2015 to 2018. These correspond to integrated luminosities of around 140  fb^{-1} for each experiment, at a center-of-mass energy of 13 TeV. The measured signal yield is 2.2±0.7 times the standard model prediction, and agrees with the theoretical expectation within 1.9 standard deviations.