  In a recent paper, A. Libgober showed that the multiplicative sequence
{Q_i(c_1,...,c_i)} of Chern classes corresponding to the power series
Q(z)=1/Gamma(1+z) appears in a relation between the Chern classes of certain
Calabi-Yau manifolds and the periods of their mirrors. We show that the
polynomials Q_i can be expressed in terms of multiple zeta values.
