Gott time machines in the Anti-de Sitter space

In 1991 Gott presented a solution of Einstein's field equations in 2+1 dimensions with $\Lambda = 0$ that contained closed timelike curves (CTC's). This solution was remarkable because at first it did not seem to be unphysical in any other respect. Later, however, it was shown that Gott's solution is tachyonic in a certain sense. Here the case $\Lambda < 0$ is discussed. We show that it is possible to construct CTC's also in this case, in a way analogous to that used by Gott. We also show that this construction still is tachyonic. $\Lambda < 0$ means that we are dealing with Anti-de Sitter space, and since the CTC-construction necessitates some understanding of its structure, a few pages are devoted to this subject.