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 s=13TeV are used, corresponding to an integrated luminosity of 36.1fb−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¯ and Z+jets production. A neural network is used to improve the background rejection and extract the signal. The resulting significance is 4.2σ in the data and the expected significance is 5.4σ. The measured cross-section for tZq production is 600±170(stat.)±140(syst.)fb.