  In this paper, we propose a conformally covariant momentum space
representation of CFT correlation functions. We call it the AdS S-matrix. This
representation has the property that it reduces to the S-matrix in the flat
space limit. The flat space limit in question is taken by keeping all the
particle masses fixed as the operator conformal dimensions go to infinity along
with the AdS radius $\mathtt{R}$. We give Feynman-like rules to compute the AdS
S-matrix in $1/ \mathtt{R}$ perturbation theory. Moreover, we relate it to the
Mellin space representation of the conformal correlators in $1/ \mathtt{R}$
perturbation theory.
