  We present a general method of folding an integrable spin chain, defined on a
line, to obtain an integrable open spin chain, defined on a half-line. We
illustrate our method through two fundamental models with sl(2) Lie algebra
symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We
obtain new long-range boundary Hamiltonians and demonstrate that they exhibit
Yangian symmetries, thus ensuring integrability of the models we obtain. The
method presented provides a "bottom-up" approach for constructing integrable
boundaries and can be applied to any spin chain model.
