  In the minimal SUGRA model the lighter tau slepton is expected to be the
second lightest superparticle over a large parameter range at large
$\tan\beta$. Consequently one expects a viable SUGRA signal at LHC in the tau
lepton channel coming from the decay of these tau sleptons. The model predicts
the polarization of this tau lepton to be +1 to a very good accuracy. We show
how this prediction can be tested by looking at the momentum fraction of the
tau-jet, carried by the charged prong, in its 1-prong hadronic decay channel.
