  If neutral Higgs bosons will be discovered at the CERN Large Hadron Collider
(LHC) then an important subsequent issue will be the investigation of their CP
nature. Higgs boson decays into tau lepton pairs are particularly suited in
this respect. Analyzing the three charged pion decay modes of the tau leptons
and taking expected measurement uncertainties at the LHC into account, we show
that the CP properties of a Higgs boson can be pinned down with appropriately
chosen observables, provided that sufficiently large event numbers will
eventually be available.
