Bose-Einstein correlations in W-pair production at LEP are investigated in a data sample of 629 pb−1 collected by the L3 detector at √s = 189–209 GeV. Bose–Einstein correlations between pions within a W decay are observed and found to be in good agreement with those in light-quark Z decay. No evidence is found for Bose–Einstein correlations between hadrons coming from different W’s in the same event.