  We show that the XYZ spin chain along the special line of couplings
J_xJ_y+J_xJ_z+J_yJ_z=0 possesses a hidden N=(2,2) supersymmetry. This lattice
supersymmetry is non-local and changes the number of sites. It extends to the
full transfer matrix of the corresponding eight-vertex model. In particular, it
is shown how to derive the supercharges from Baxter's Bethe ansatz. This
analysis leads to new conjectures concerning the ground state for chains of odd
length. We also discuss a correspondence between the spectrum of this XYZ chain
and that of a manifestly supersymmetric staggered fermion chain.
