  The spectrum of a one-dimensional chain of $SU(n)$ spins positioned at the
static equilibrium positions of the particles in a corresponding classical
Calogero system with an exchange interaction inversely proportional to the
square of their distance is studied. As in the translationally invariant
Haldane--Shastry model the spectrum is found to exhibit a very simple structure
containing highly degenerate ``super-multiplets''. The algebra underlying this
structure is identified and several sets of raising and lowering operators are
given explicitely. On the basis of this algebra and numerical studies we give
the complete spectrum and thermodynamics of the $SU(2)$ system.
