  Using Gross-Pitaevskii equation, we study the time reversibility of
Bose-Einstein condensates (BEC) in kicked optical lattices, showing that inside
the regime of quantum chaos the dynamics can be inverted from explosion to
collapse. The accuracy of time reversal decreases with the increase of atom
interactions inside BEC, until it is completely lost. Surprisingly, quantum
chaos helps to restore time reversibility. These predictions can be tested with
existing experimental setups.
