Must time-machine construction violate the weak energy condition?

We present a time-machine model in which closed timelike curves evolve, within a bounded region of space, from a well-behaved spacelike initial slice S; this slice (and the entire spacetime) is asymptotically flat and topologically trivial. In addition, this model satisfies the weak energy condition everywhere on S and up until and beyond the time slice (an achronal hypersurface) which displays the causality violation. We discuss the relation of this model to theorems by Tipler and Hawking which place constraints on time-machine solutions.