  The Hamiltonian governing the gravitational interaction of N relativistic
particles in a four-dimensional anti-de Sitter background is derived to leading
order in Newton's constant. The resulting pairwise interactions, combined with
the confining nature of motion in anti-de Sitter spacetime, are expected to
lead to classical chaos. In the context of the AdS/CFT correspondence, the
emergence of a chaotic classical limit on the gravity side has important
implications for the dual three-dimensional conformal field theory, including
that the spectrum of conformal primary operators at strong coupling should
exhibit level repulsion in line with the Wigner surmise.
