  We show that the averaged null energy condition can be violated by a
conformally coupled scalar field in a conformally flat spacetime in 3+1
dimensions. The violation is dependent on the quantum state and can be made as
large as desired. It does not arise from the presence of anomalies, although
anomalous violations are also possible. Since all geodesics in conformally flat
spacetimes are achronal, the achronal averaged null energy condition is
likewise violated.
