  We study a linear spin chain which was originally introduced by Shi et al.
[Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength
contains a parameter $\alpha$ and depends on the parity of the chain site.
Extending the model by a second parameter $\beta$, it is shown that the single
fermion eigenstates of the Hamiltonian can be computed in explicit form. The
components of these eigenvectors turn out to be Hahn polynomials with
parameters $(\alpha,\beta)$ and $(\alpha+1,\beta-1)$. The construction of the
eigenvectors relies on two new difference equations for Hahn polynomials. The
explicit knowledge of the eigenstates leads to a closed form expression for the
correlation function of the spin chain. We also discuss some aspects of a
$q$-extension of this model.
