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We present a measurement of the top quark mass in the dilepton channel based on approximately 370 pb-1 of data collected by the DØ experiment during Run II of the Fermilab Tevatron collider. We employ two different methods to extract the top quark mass. We show that both methods yield consistent results using ensemble tests of events generated with the DØ Monte Carlo simulation. We combine the results from the two methods to obtain a top quark mass mt = 178.1 ± 8.2 GeV. The statistical uncertainty is 6.7 GeV and the systematic uncertainty is 4.8 GeV.