  The complete one-loop, planar dilatation operator of the N=4 superconformal
gauge theory was recently derived and shown to be integrable. Here, we present
further compelling evidence for a generalisation of this integrable structure
to higher orders of the coupling constant. For that we consider the su(2|3)
subsector and investigate the restrictions imposed on the spin chain
Hamiltonian by the symmetry algebra. This allows us to uniquely fix the energy
shifts up to the three-loop level and thus prove the correctness of a
conjecture in hep-th/0303060. A novel aspect of this spin chain model is that
the higher-loop Hamiltonian, as for N=4 SYM in general, does not preserve the
number of spin sites. Yet this dynamic spin chain appears to be integrable.
