  We explore the prospects for searches at the LHC for sparticle decays that
violate $\tau$ lepton number, in the light of neutrino oscillation data and the
seesaw model for neutrino masses and mixing. We analyse the theoretical and
phenomenological conditions required for tau flavour violation to be observable
in \chi_2 \to \chi + \tau^\pm \mu^\mp decays, for cosmologically interesting
values of the relic neutralino LSP density. We study the relevant
supersymmetric parameter space in the context of the Constrained Minimal
Supersymmetric Extension of the Standard Model (CMSSM) and in SU(5) extensions
of the theory. We pay particular attention to the possible signals from
hadronic tau decays, that we analyse using PYTHIA event simulation. We find
that a signal for \tau flavour-violating \chi_2 decays may be observable if the
branching ratio exceeds about 10%. This may be compatible with the existing
upper limit on \tau \to \mu \gamma decays if there is mixing between
right-handed sleptons, as could be induced in non-minimal SU(5) GUTs.
