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We present the first observation in hadronic collisions of the electroweak production of vector boson pairs (VV, V=W, Z) where one boson decays to a dijet final state. The data correspond to 3.5  fb-1 of integrated luminosity of pp̅ collisions at √s=1.96  TeV collected by the CDF II detector at the Fermilab Tevatron. We observe 1516±239(stat)±144(syst) diboson candidate events and measure a cross section σ(pp̅ →VV+X) of 18.0±2.8(stat)±2.4(syst)±1.1(lumi)  pb, in agreement with the expectations of the standard model.