A measurement is presented of the cross section for the electroweak production of a Z boson and a photon in association with two jets in proton-proton collisions at sqrt(s)= 8 TeV. The Z bosons are identified through their decays to electron or muon pairs. The measurement is based on data collected with the CMS detector corresponding to an integrated luminosity of 19.7 inverse femtobarns. The electroweak contribution has a significance of 3.0 standard deviations, and the measured fiducial cross section is 1.86 +0.90/-0.75 (stat) +0.34/-0.26 (syst) +/- 0.05 (lumi) fb, while the summed electroweak and quantum chromodynamic total cross section in the same region is observed to be 5.94 +1.53/-1.35 (stat) +0.43/-0.37 (syst) +/- 0.13 (lumi) fb. Both measurements are consistent with the leading-order standard model predictions. Limits on anomalous quartic gauge couplings are set based on the Z gamma mass distribution.