The production of a top quark in association with a Z boson is investigated. The proton-proton collision data collected by the ATLAS experiment at the LHC in 2015 and 2016 at a centre-of-mass energy of root s = 13 TeV are used, corresponding to an integrated luminosity of 36.1 fb(-1). Events containing three identified leptons (electrons and/or muons) and two jets, one of which is identified as a b-quark jet are selected. The major backgrounds are diboson, tt($)over-bar and Z + jets production. A neural network is used to improve the background rejection and extract the signal. The resulting significance is 4.2 sigma in the data and the expected significance is 5.4 sigma. The measured cross-section for tZq production is 600 +/- 170(stat.)+/- 140(syst.)fb.