  Let $X$ be an arbitrary smooth $n$-dimensional projective variety. It was
discovered by Libgober and Wood that the product of the Chern classes
$c_1(X)c_{n-1}(X)$ depends only on the Hodge numbers of $X$. This result has
been used by Eguchi, Jinzenji and Xiong in their approach to the quantum
cohomology of $X$ via a representation of the Virasoro algebra with the central
charge $c_n(X)$. In this paper we define for singular varieties $X$ a rational
number $c_{st}^{1,n-1}(X)$ which is a stringy version of the number
$c_1c_{n-1}$ for smooth $n$-folds. We show that the number $c_{st}^{1,n-1}(X)$
can be expressed in the same way using the stringy Hodge numbers of $X$. Our
results provides an evidence for the existence of an approach to quantum
cohomology of singular varieties $X$ via a representation of the Virasoro
algebra whose central charge is the rational number $e_{st}(X)$ which equals
the stringy Euler number of $X$.
