  We use computer algebra to demonstrate the existence of a multilinear
polynomial identity of degree 8 satisfied by the bilinear operation in every
Lie-Yamaguti algebra. This identity is a consequence of the defining identities
for Lie-Yamaguti algebras, but is not a consequence of anticommutativity. We
give an explicit form of this identity as an alternating sum over all
permutations of the variables in a polynomial with 8 terms. Our computations
also show that such identities do not exist in degrees less than 8.
