We give a procedure for deriving certain bulk S-matrix elements from corresponding boundary correlators. These are computed in the plane-wave limit, via an explicit construction of certain boundary sources that give bulk wave packets. A critical role is played by a specific singular behavior of the Lorentzian boundary correlators. It is shown in examples how correlators derived from the bulk supergravity exhibit the appropriate singular structure, and reproduce the corresponding S-matrix elements. This construction thus provides a nontrivial test for whether a given boundary conformal field theory can reproduce bulk physics, and where it does, supplies a prescription to extract bulk S-matrix elements in the plane-wave limit.