  This Letter presents a measurement of the $\WW$ production cross section in
$\sqrt{s} = 7 \TeV\ pp$ collisions by the ATLAS experiment, using 34 $\pbi$ 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 $1.7\pm0.6$
events. The measured cross section is $41^{+20}_{-16}(\mathrm{stat.})\pm
5(\mathrm{syst.})\pm 1(\mathrm{lumi.})$ pb, which is consistent with the
standard model prediction of $44 \pm 3$ pb calculated at next-to-leading order
in QCD.
