The first measurement of the cross section for top-quark pair production in pp collisions at the Large Hadron Collider at center-of-mass energy inline image has been performed using a data sample corresponding to an integrated luminosity of 3.1+/-0.3 pb super(-1) recorded by the CMS detector. This result utilizes the final state with two isolated, highly energetic charged leptons, large missing transverse energy, and two or more jets. Backgrounds from Drell-Yan and non-W/Z boson production are estimated from data. Eleven events are observed in the data with 2.1+/-1.0 events expected from background. The measured cross section is 194+/-72(stat.)+/-24(syst.)+/-21(lumi.) pb, consistent with next-to-leading order predictions.