A search for flavour changing neutral current (FCNC) processes in top-quark decays by the ATLAS Collaboration is presented. Data collected from pp collisions at the LHC at a centre-of-mass energy of root s = 7 TeV during 2011, corresponding to an integrated luminosity of 2.1 fb(-1), were used. A search was performed for top-quark pair-production events, with one top quark decaying through the t -> Zq FCNC (q = u, c) channel, and the other through the Standard Model dominant mode t -> Wb. Only the decays of the Z boson to charged leptons and leptonic W-boson decays were considered as signal. Consequently, the final-state topology is characterised by the presence of three isolated charged leptons, at least two jets and missing transverse momentum from the undetected neutrino. No evidence for an FCNC signal was found. An upper limit on the t -> Zq branching ratio of BR(t -> Zq) < 0.73% is set at the 95% confidence level.