Gott time machines in anti-deSitter 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 also possible to construct CTC's in this case, in a way analogous to that used by Gott. We also show a special case of this construction to be 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.