The first search for a heavy charged vector boson in the final state with a tau lepton and a neutrino is reported, using 19.7 fb−1 of LHC data at s=8 TeV. A signal would appear as an excess of events with high transverse mass, where the standard model background is low. No excess is observed. Limits are set on a model in which the W′ decays preferentially to fermions of the third generation. These results substantially extend previous constraints on this model. Masses below 2.0 to 2.7 TeV are excluded, depending on the model parameters. In addition, the existence of a W′ boson with universal fermion couplings is excluded at 95% confidence level, for W′ masses below 2.7 TeV. For further reinterpretation a model-independent limit on potential signals for various transverse mass thresholds is also presented.