  We demonstrate that a completely integrable classical mechanical model,
namely the lattice Landau-Lifshitz classical spin chain, supports diffusive
spin transport with a finite diffusion constant in the easy-axis regime, while
in the easy-plane regime it displays ballistic transport in the absence of any
known relevant local or quasi-local constant of motion in the symmetry sector
of the spin current. This surprising finding should open the way towards
analytical computation of diffusion constants for integrable interacting
systems and hints on existence of new quasi-local classical conservation laws
beyond the standard soliton theory.
