  We construct the supersymmetric nonlinear sigma model in a fixed AdS_5
background. We use component fields and find that the complex bosons must be
the coordinates of a hyper-Kahler manifold that admits a Killing vector
satisfying an inhomogeneous tri-holomorphic condition. We propose boundary
conditions that map the on-shell bulk hypermultiplets into off-shell chiral
multiplets on 3-branes that foliate the bulk. The supersymmetric AdS_5
isometries reduce to superconformal transformations on the brane fields.
