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 s= 7 TeV. Events containing either four charged leptons (ℓ ℓ ℓ ℓ) or two charged leptons and two jets (ℓ ℓ 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 Randall–Sundrum (RS1) graviton model as a benchmark. Using both ℓ ℓ ℓ ℓ and ℓ ℓ j j events, an RS1 graviton with k/m¯ pl= 0.1 and mass between 325 and 845 GeV is excluded at 95% confidence level. In addition, the ℓ ℓ ℓ ℓ events are used to set a model-independent fiducial cross section limit of σ fid (p p→ X→ ZZ)< 0.92 pb at 95% confidence level for any new sources of ZZ production with m ZZ greater than 300 GeV.