  We construct a new exactly solvable supersymmetric spin chain related to the
BC_N extended root system, which includes as a particular case the BC_N version
of the Polychronakos-Frahm spin chain. We also introduce a supersymmetric spin
dynamical model of Calogero type which yields the new chain in the large
coupling limit. This connection is exploited to derive two different
closed-form expressions for the chain's partition function by means of
Polychronakos's freezing trick. We establish a boson-fermion duality relation
for the new chain's spectrum, which is in fact valid for a large class of (not
necessarily integrable) spin chains of BC_N type. The exact expressions for the
partition function are also used to study the chain's spectrum as a whole,
showing that the level density is normally distributed even for a moderately
large number of particles. We also determine a simple analytic approximation to
the distribution of normalized spacings between consecutive levels which fits
the numerical data with remarkable accuracy. Our results provide further
evidence that spin chains of Haldane-Shastry type are exceptional integrable
models, in the sense that their spacings distribution is not Poissonian, as
posited by the Berry-Tabor conjecture for "generic'' quantum integrable
systems.
