We present a measurement of the top quark pair (t t¯) production cross section in pp¯ collisions at √s = 1.96 TeV using events with two charged leptons in the final state. This analysis utilizes an integrated luminosity of 224–243 pb−1 collected with the DØ detector at the Fermilab Tevatron Collider. We observe 13 events in the e+e−, eμ and μ+μ− channels with an expected background of 3.2 ± 0.7 events. For a top quark mass of 175 GeV, we measure a t ¯t production cross section of σt ¯t = 8.6+3.2 −2.7(stat) ± 1.1(syst)± 0.6(lumi) pb, consistent with the standard model prediction.