  We introduce four types of SU(2M+1) spin chains which can be regarded as the
BC_N versions of the celebrated Haldane-Shastry chain. These chains depend on
two free parameters and, unlike the original Haldane-Shastry chain, their sites
need not be equally spaced. We prove that all four chains are solvable by
deriving an exact expression for their partition function using Polychronakos's
"freezing trick". From this expression we deduce several properties of the
spectrum, and advance a number of conjectures that hold for a wide range of
values of the spin M and the number of particles. In particular, we conjecture
that the level density is Gaussian, and provide a heuristic derivation of
general formulas for the mean and the standard deviation of the energy.
