We present the first observation of exclusive e+e− production in hadron-hadron collisions, using pp collision data at s√=1.96  TeV taken by the run II Collider Detector at Fermilab, and corresponding to an integrated luminosity of 532  pb−1. We require the absence of any particle signatures in the detector except for an electron and a positron candidate, each with transverse energy ET>5  GeV and pseudorapidity |η|<2. With these criteria, 16 events are observed compared to a background expectation of 1.9±0.3 events. These events are consistent in cross section and properties with the QED process pp→p+e+e−+p through two-photon exchange. The measured cross section is 1.6+0.5−0.3(stat)±0.3(syst)  pb. This agrees with the theoretical prediction of 1.71±0.01  pb.