  We apply the $AdS/CFT$ holography to the simplest possible eternal time
machine solution in $AdS_3$ based on two conical defects moving around their
center of mass along a circular orbit. Closed timelike curves in this
space-time extend all the way to the boundary of $AdS_3$, violating causality
of the boundary field theory. By use of the geodesic approximation we address
the "grandfather paradox" in the dual $1+1$ dimensional field theory and
calculate the two-point retarded Green function. It has a non-trivial
analytical structure both at negative and positive times, providing us with an
intuition on how an interacting quantum field could behave once causality is
broken. In contrast with the previous considerations our calculations reveal
the possibility of a consistent and controllable evolution of a quantum system
without any need to impose additional consistency constraints.
