  Measurements in $W^+W^-$ events at LEP2 and in $B$ hadron semileptonic decays
at B factories and LHCb provide intriguing hints of a violation of lepton
universality in the charged current coupling of tau leptons relative to those
for electrons and muons. We propose a novel, self-calibrating method to test
tau lepton universality in $W$ boson decays at the LHC. We compare directly the
ratio of the numbers of selected $\ell-\tau$ and $e-\mu$ final states in
di-leptonic $tt$ events with that in $Z/\gamma^*\rightarrow\tau^+\tau^-$
events. Here $\ell=e$ or $\mu$ and $\tau$ is a candidate semi-hadronic tau
decay. This "double-ratio" cancels to first order sensitivity to systematic
uncertainties on the reconstruction of $e$, $\mu$, and $\tau$ leptons, thus
improving very significantly the precision to which tau lepton universality can
be tested in $W$ boson decay branching ratios at the LHC. Using particle-level
Monte Carlo events, and a parameterised simulation of detector performance, we
demonstrate the effectiveness of the method and estimate the most significant
residual sources of uncertainty arising from experimental and phenomenological
systematics. Our studies indicate that a single experiment precision on the tau
lepton universality test of around 1.4% is achievable with a data set of 140
fb$^{-1}$ at $\sqrt{s}$ = 13 TeV. This would improve significantly upon the
precision of 2.5% on the four-experiment combined LEP2 measurements. If the
central value of the proposed new measurement were equal to the central value
of the LEP2 measurement this would yield an observation of BSM physics at a
significance level of around 5 $\sigma$.
