Using 1.1 fb-1 of data collected by the Collider Detector at Fermilab (CDF) from Run II of the Fermilab Tevatron, we measure the tt production cross section in events with two leptons, significant missing transverse energy, and & ge;2 jets. As the Run II dataset grows, more stringent tests of Standard Model predictions for the top quark sector are becoming possible. The dilepton channel, where both top quarks decay t & rarr; Wb & rarr; & ell;nu b, is of particular interest due to its high purity even in the absence of a b jet "tagging" requirement. Use of an isolated track as the second lepton significantly increases the dilepton acceptance, at the price of some increase in background, particularly from W + jets events where one of the jets is identified as a lepton. With the amount of data available, it has been possible to improve the estimate of the contribution from that background, reflected in a reduced systematic uncertainty. Assuming a branching ratio of BR(W & rarr; & ell;nu) = 10.8% and a top mass of mt = 175 GeV/ c2, the measured cross-section is sigma(pp & rarr; tt) + 8.3 +/- 1.3(stat.) +/- 0.7(syst.) +/- 0.5(lumi.) pb. The result is consistent with the Standard Model prediction of 6.7+0.7-0.9 pb and represents a significant improvement in precision over previous results using this selection.