  We have performed an experiment to demonstrate the approximate time reversal
of a "chaotic" time evolution of atomic deBroglie waves. We use ultra cold
atoms from a Bose-Einstein condensate in a quantum $\delta$-kicked rotor
experiment, and show that an initial state can be approximately re-created even
after a period of "chaotic" evolution (a number of kicks). As this mechanism
only works for a very narrow range of momenta, the net effect is a narrowing of
the momentum distribution after the kick sequence.
