  We study the simplest two-body problem in asymptotically anti-de Sitter
spacetime: two, infinitely thin, concentric spherical shells of matter. We
include only gravitational interaction between the two shells, but we show that
the dynamics of this system is highly nontrivial. We observe prompt collapse to
a black hole, delayed collapse and even perpetual oscillatory motion, depending
on the initial location of the shells (or their energy content). The system
exhibits critical behavior, and we show strong hints that it is also chaotic.
