We present a measurement of the top quark mass in the dilepton channel based on approximately 370/pb of data collected by the D0 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 D0 Monte Carlo simulation. We combine the results from the two methods to obtain a top quark mass m_t = 178.1 +/- 8.2 GeV. The statistical uncertainty is 6.7 GeV and the systematic uncertainty is 4.8 GeV.