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A search is presented for a narrow resonance decaying to a pair of Z bosons using data corresponding to 1.02 fb(-1) of integrated luminosity collected by the ATLAS experiment from pp collisions at root s= 7 TeV. Events containing either four charged leptons (llll) or two charged leptons and two jets (lljj) are analyzed and found to be consistent with the Standard Model background expectation. Lower limits on a resonance mass are set using the Randall-Sundrum (RS1) graviton model as a benchmark. Using both llll and lljj events, an RS1 graviton with k/(m) over bar (pl) = 0.1 and mass between 325 and 845 GeV is excluded at 95% confidence level. In addition, the llll events are used to set a model-independent fiducial cross section limit of sigma(fid)(pp -> X -> ZZ) < 0.92 pb at 95% confidence level for any new sources of ZZ production with m(ZZ) greater than 300 GeV.