Precision Measurement of the Ratio <math><mrow><mi>B</mi><mo>(</mo><mi>ϒ</mi><mo>(</mo><mn>3</mn><mi>S</mi><mo>)</mo><mo>→</mo><msup><mrow><mi>τ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo><mo>/</mo><mi>B</mi><mo>(</mo><mi>ϒ</mi><mo>(</mo><mn>3</mn><mi>S</mi><mo>)</mo><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>)</mo></mrow></math>

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&#177;0.008stat&#177;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.