The branching fraction ratio R(D∗)≡B(B¯0→D*+τ−ν¯τ)/B(B¯0→D*+μ−ν¯μ) is measured using a sample of proton-proton collision data corresponding to 3.0  fb−1 of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode τ−→μ−ν¯μντ. The semitauonic decay is sensitive to contributions from non-standard-model particles that preferentially couple to the third generation of fermions, in particular, Higgs-like charged scalars. A multidimensional fit to kinematic distributions of the candidate B¯0 decays gives R(D∗)=0.336±0.027(stat)±0.030(syst). This result, which is the first measurement of this quantity at a hadron collider, is 2.1 standard deviations larger than the value expected from lepton universality in the standard model.