  It is well-known that a hypothetical particle which moves faster than the
light, a \emph{tachyon}, is unstable in the Minkowski space-time. Here we shall
show that, contrary to the Minkowski case, the tachyon is stable in the
rotating Universe described by a family of the G\"{o}del-like solutions, unless
the absolute value of its mass is larger than some small constant which is
related to the universe`s rotation scale and is many orders less than the
electron`s mass. The smallness of this upper bound on the tachyon`s mass might
be an explanation why we do not observe heavy tachyons. Mathematically, the
stability bound is similar to the well-known Breitenlohner-Freedman bound for
the asymptotically anti-de Sitter (AdS) space-times.
