This Letter reports evidence of triple gauge boson production pp→W(ℓν)γγ+X, which is accessible for the first time with the 8 TeV LHC data set. The fiducial cross section for this process is measured in a data sample corresponding to an integrated luminosity of 20.3 fb^{-1}, collected by the ATLAS detector in 2012. Events are selected using the W boson decay to eν or μν as well as requiring two isolated photons. The measured cross section is used to set limits on anomalous quartic gauge couplings in the high diphoton mass region.