A search is presented for a narrow resonance decaying to a pair of Z bosons using data corresponding to 1.02 fb−11.02 fb−1 of integrated luminosity collected by the ATLAS experiment from pp collisions at √s=7 TeV. Events containing either four charged leptons (ℓℓℓℓℓℓℓℓ) or two charged leptons and two jets (ℓℓjjℓℓjj) 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 ℓℓℓℓℓℓℓℓ and ℓℓjjℓℓjj events, an RS1 graviton with k/mpl=0.1 and mass between 325 and 845 GeV is excluded at 95%95% confidence level. In addition, the ℓℓℓℓℓℓℓℓ events are used to set a model-independent fiducial cross section limit of σfid(pp→X→ZZ)<0.92pb at 95% confidence level for any new sources of ZZ production with mZZmZZ greater than 300 GeV.