The CDF and D0 collaborations have updated their measurements of the mass of the top quark using proton-antiproton collisions at s**(1/2) = 1.96 TeV produced at the Tevatron. The uncertainties in each of the top-antitop decay channels have been reduced. The new Tevatron average for the mass of the top quark based on about 1 fb-1 of data per experiment is 170.9 +/- 1.8 GeV/c2.