Using data collected with the CLEO III detector at the CESR e+e- collider, we report on a first observation of the decay Upsilon(3S)-->tau+tau-, and precisely measure the ratio of branching fractions of Upsilon(nS), n=1, 2, 3, to tau+tau- and mu+mu- final states, finding agreement with expectations from lepton universality. We derive absolute branching fractions for these decays, and also set a limit on the influence of a low mass CP-odd Higgs boson in the decay of the Upsilon(1S).