  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.
