  This Letter reports a measurement of the WW production cross section in
sqrt(s) = 7 TeV pp collisions using data corresponding to an integrated
luminosity of 1.02/fb collected with the ATLAS detector. Using leptonic decays
of oppositely charged W bosons, the total measured cross section is sigma(pp ->
WW) = 54.4 +/- 4.0 (stat.) +/- 3.9 (syst.) +/- 2.0 (lumi.) pb, consistent with
the Standard Model prediction of sigma(pp -> WW) = 44.4 +/- 2.8 pb. Limits on
anomalous electroweak triple-gauge couplings are extracted from a fit to the
transverse-momentum distribution of the leading charged lepton in the event.
