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We consider the ground state of the XY model on an infinite chain at zero temperature. Following Bennett, Bernstein, Popsecu and Schumacher we use entropy of a subsystem as a measure of entanglement. Vidal, Latorre, Rico and Kitaev conjectured that von Neumann entropy of a large block of neighboring spins approaches a constant as the size of the block increases. We evaluated this limiting entropy as a function of anisotropy and transverse magnetic field. We used the methods based on integrable Fredholm operators and Riemann-Hilbert problem. This is joint work with B.-Q. Jin and V. E. Korepin.