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