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.