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We report a measurement of the tt̅ production cross section using dilepton events with jets and missing transverse energy in pp̅ collisions at a center-of-mass energy of 1.96 TeV. Using a 197±12 pb-1 data sample recorded by the upgraded Collider Detector at Fermilab, we use two complementary techniques to select candidate events. We compare the number of observed events and selected kinematical distributions with the predictions of the standard model and find good agreement. The combined result of the two techniques yields a tt̅ production cross section of 7.0-2.1+2.4 (stat) -1.1+1.6 (syst)±0.4(lum) pb.