  A space consisting of two rapidly moving cosmic strings has recently been
constructed by Gott that contains closed timelike curves. The global structure
of this space is analysed and is found that, away from the strings, the space
is identical to a generalised Misner space. The vacuum expectation value of the
energy momentum tensor for a conformally coupled scalar field is calculated on
this generalised Misner space. It is found to diverge very weakly on the
Chronology horizon, but more strongly on the polarised hypersurfaces. The
divergence on the polarised hypersurfaces is strong enough that when the proper
geodesic interval around any polarised hypersurface is of order the Planck
length squared, the perturbation to the metric caused by the backreaction will
be of order one. Thus we expect the structure of the space will be radically
altered by the backreaction before quantum gravitational effects become
important. This suggests that Hawking's `Chronology Protection Conjecture'
holds for spaces with non-compactly generated Chronology horizon.
