  We demonstrate that certain supersymmetric Goedel-like universe solutions of
supergravity are not solutions of string theory. This is achieved by realizing
that supertubes are BPS states in these spaces, and under certain conditions,
when wrapping closed timelike curves, some world-volume modes develop negative
kinetic terms. Since these universes are homogeneous, this instability takes
place everywhere in space-time. We also construct a family of supergravity
solutions which locally look like the Goedel universe inside a domain wall made
out of supertubes, but have very different asymptotic structure. One can adjust
the volume inside the domain wall so there will be no closed timelike curves,
and then those spaces seem like perfectly good string backgrounds.
