This Letter presents a measurement of the W+W− production cross section in √s=7  TeV pp collisions by the ATLAS experiment, using 34  pb−1 of integrated luminosity produced by the Large Hadron Collider at CERN. Selecting events with two isolated leptons, each either an electron or a muon, 8 candidate events are observed with an expected background of 1.7±0.6 events. The measured cross section is 41+20−16(stat)±5(syst)±1(lumi)  pb, which is consistent with the standard model prediction of 44±3  pb calculated at next-to-leading order in QCD.