Some results are obtained which establish conditions under which causality violation cannot occur in space-times admitting a compact, but not necessarily acausal, spacelike hypersurface. For example, it is shown that causality violation can occur in a space-time admitting a compact spacelike slice and obeying fairly reasonable energy conditions only if it is “singular” in the sense that some “causal interval”J+(p) ∩J−(q) has noncompact closure.