  We consider teleportation of an arbitrary spin-1/2 target quantum state along
the ground state of a quantum spin chain. We present a decomposition of the
Hilbert space of the many body quantum state into 4 vector spaces. Within each
of these subspaces, it is possible to take any superposition of states, and use
projective measurements to perform unit fidelity teleportation. Any such
superposition is necessarily a spin liquid state. We also show that all total
spin-0 quantum states belong in the same space, so that it is possible to
perform unit fidelity teleportation over any one-dimensional spin-0 many body
quantum state. We generalise to $n$-Bell states, and present some general
bounds on fidelity of teleportation given a general state of a quantum spin
chain.
