  We study a CP-violating triple product correlation that occurs in the decay
of a neutral Higgs boson into t\bar{t} pairs when the Higgs boson does not have
a definite CP nature. We consider the H -> t \bar{t} decay channel as well as
the gluon fusion process gg -> H -> t \bar{t}. The asymmetry in Higgs decay,
normalized to the H -> t \bar{t} width, can reach the 6% percent level. In the
gluon fusion process the corresponding normalized asymmetry is smaller by an
order of magnitude. We present a crude estimate of this observable at the LHC.
