We investigate the instability of the Cauchy horizon caused by causality<br />
violation in the compact vacuum universe with the topology $B\times {\bf<br />
S}^{1}\times {\bf R}$, which Moncrief and Isenberg considered. We show that if<br />
the occurrence of curvature singularities are restricted to the boundary of<br />
causality violating region, the whole segments of the boundary become curvature<br />
singularities. This implies that the strong cosmic censorship holds in the<br />
spatially compact vacuum space-time in the case of the causality violation.<br />
This also suggests that causality violation cannot occur for a compact<br />
universe.