We report on a precision measurement of the ratio RτμΥ(3S)=B(Υ(3S)→τ+τ-)/B(Υ(3S)→μ+μ-) using data collected with the BABAR detector at the SLAC PEP-II e+e- collider. The measurement is based on a 28 fb-1 data sample collected at a center-of-mass energy of 10.355 GeV corresponding to a sample of 122 million Υ(3S) mesons. The ratio is measured to be RτμΥ(3S)=0.966±0.008stat±0.014syst and is in agreement with the standard model prediction of 0.9948 within 2 standard deviations. The uncertainty in RτμΥ(3S) is almost an order of magnitude smaller than the only previous measurement.