  For the elliptic Gaudin model (a degenerate case of XYZ integrable spin
chain) a separation of variables is constructed in the classical case. The
corresponding separated coordinates are obtained as the poles of a suitably
normalized Baker-Akhiezer function. The classical results are generalized to
the quantum case where the kernel of separating integral operator is
constructed. The simplest one-degree-of-freedom case is studied in detail.
