We present an analysis of dilepton events originating from ttbar
production in ppbar 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 nine 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).