We obtain the exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ model, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then we consider the anisotropic scaling limit of the XYZ chain that yields the 1+1 dimensional sine-Gordon model. We present the formula for the entanglement entropy of the latter, which has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory.