  We show the factorization of the three-particle world-sheet S-matrix of AdS_5
x S^5 superstring theory in the near-flat-space limit at one loop order. This
is done by computing various scattering amplitudes from Feynman diagrams in the
world-sheet theory. The knowledge of certain highest weight amplitudes allows
us to fix all the freedom in the three-particle S-matrix, which we argue to be
constrained up to four scalar functions due to the symmetries of the model. We
demonstrate that these amplitudes are given by corresponding products of the
known two-particle S-matrix elements, from which it follows that the scattering
of any three world-sheet excitations factorizes. This provides an explicit and
direct check of the quantum integrability of string theory in near-flat AdS_5 x
S^5 as it renders evidence for the existence of higher conserved charges. By
computing further amplitudes we also obtain an indirect confirmation of the
supersymmetries of the near-flat-space model.
