  2+1 dimensional anti-de Sitter space has been the subject of much recent
investigation. Studies of the behaviour of point particles in this space have
given us a greater understanding of the BTZ black hole solutions produced by
topological identification of adS isometries. In this paper, we present a new
configuration of two orbiting massive point particles that leads to an
``eternal'' time machine, where closed timelike curves fill the entire space.
In contrast to previous solutions, this configuration has no event or
chronology horizons. Another interesting feature is that there is no lower
bound on the relative velocities of the point masses used to construct the time
machine; as long as the particles exceed a certain mass threshold, an eternal
time machine will be produced.
