  We demonstrate that the one-loop dilatation generator for the scalar sector
of a certain perturbation of N=4 Super Yang-Mills with fundamentals is the
Hamiltonian of an integrable spin chain with open boundary conditions. The
theory is a supersymmetric defect conformal field theory (dCFT) with the
fundamentals in hypermultiplets confined to a codimension one defect. We obtain
a K-matrix satisfying a suitably generalized form of the boundary Yang-Baxter
equation, study the Bethe ansatz equations and demonstrate how Dirichlet and
Neumann boundary conditions arise in field theory, and match to existing
results in the plane wave limit.
