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We compute the entropy of entanglement between the first $N$ spins and therest of the system in the ground states of a general class of quantumspin-chains. We show that under certain conditions the entropy can be expressedin terms of averages over ensembles of random matrices. These averages can beevaluated, 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 thecentral charge.Comment: 4 page

Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory