  We compute the entropy of entanglement between the first $N$ spins and the
rest of the system in the ground states of a general class of quantum
spin-chains. We show that under certain conditions the entropy can be expressed
in terms of averages over ensembles of random matrices. These averages can be
evaluated, allowing us to prove that at critical points the entropy grows like
$\kappa\log_2 N + {\tilde \kappa}$ as $N\to\infty$, where $\kappa$ and ${\tilde
\kappa}$ are determined explicitly. In an important class of systems, $\kappa$
is equal to one-third of the central charge of an associated Virasoro algebra.
Our expression for $\kappa$ therefore provides an explicit formula for the
central charge.
