In this Brief Report I introduce yet another class of geometries for which semiclassical chronology protection theorems are of dubious physical reliability. I consider a ``Roman ring'' of traversable wormholes, wherein a number of wormholes are arranged in a ring in such a manner that no subset of wormholes is near chronology violation, though the combined system can be arbitrarily close to chronology violation. I show that (with enough wormholes in the ring) the gravitational vacuum polarization (the expectation value of the quantum stress-energy tensor) can be made arbitrarily small. In particular, the back reaction can be kept arbitrarily small all the way to the ``reliability horizon,'' so that semiclassical quantum gravity becomes unreliable before the gravitational back reaction becomes large.