  We analyze the production of triple pseudoscalar Higgs bosons in the decay
channel of $Z\rightarrow AAA$ for light pseudoscalar bosons when the
corresponding scalar boson is too heavy to be produced by $Z$ decay. Analytic
results are obtained both at the tree level and at the one--loop level. The
branching fraction can be as large as $10^{-5}$ which should be detectable at
LEP.
