Evidence for electroweak production of two jets in association with a Z gamma pair in root s = 13 TeV proton-proton collisions at the Large Hadron Collider is presented. The analysis uses data collected by the ATLAS detector in 2015 and 2016 that corresponds to an integrated luminosity of 36.1 fb(-1). Events that contain a Z boson candidate decaying leptonically into either e(+)e(-) or mu(+)mu(-), a photon, and two jets are selected. The electroweak component is measured with observed and expected significances of 4.1 standard deviations. The fiducial cross-section for electroweak production is measured to be sigma(Z gamma jj-Ew) = 7.8 +/- 2.0 fb, in good agreement with the Standard Model prediction.