We present an analysis of dilepton events originating from ttbar production in pbar p collisions at sqrt s = 1.8 TeV at the Fermilab Tevatron Collider. The sample corresponds to an integrated luminosity of 109 +/- 7 pb^-1. We observe 9 candidate events, with an estimated background of 2.4 +/- 0.5 events. We determine the mass of the top quark to be M_top = 161 +/- 17(stat.) +/- 10(syst.) GeV/c^2. In addition we measure a ttbar production cross section of 8.2^_+4.4_ -3.4 pb (where M_top = 175 GeV/c^2 has been assumed for the acceptance estimate).