  We examine the achronal averaged null energy condition~(ANEC) for a class of
conformal field theories~(CFT) at strong coupling in curved spacetime. By
applying the AdS/CFT duality, we find holographic models which violate the
achronal ANEC for $3+1$ and $4+1$-dimensional boundary theories. In our model,
the bulk spacetime is an asymptotically AdS vacuum bubble solution with neither
causality violation nor singularities. The conformal boundary of our bubble
solution is asymptotically flat and is causally proper in the sense that a
"fastest null geodesics" connecting any two points on the boundary must lie
entirely on the boundary. We show that conversely, if the spacetime fails to
have this causally proper nature, then there must be a naked singularity in the
bulk.
