  Analogue gravity systems offer many insights into gravitational phenomena,
both at the classical and at the semiclassical level. The existence of an
underlying Minkowskian structure (or Galilean in the non-relativistic limit) in
the laboratory has been argued to directly forbid the simulation of geometries
with Closed Timelike Curves (CTCs) within analogue systems. We will show that
this is not strictly the case. In principle, it is possible to simulate
spacetimes with CTCs whenever this does not entail the presence of a
chronological horizon separating regions with CTCs from regions that do not
have CTCs. We find an Analogue-gravity Chronology protection mechanism very
similar in spirit to Hawking's Chronology Protection hypothesis. We identify
the universal behaviour of analogue systems near the formation of such horizons
and discuss the further implications that this analysis has from an emergent
gravity perspective. Furthermore, we build explicit geometries containing CTCs,
for instance spacetimes constructed from two warp-drive configurations, that
might be useful for future analysis, both from a theoretical and an
experimental point of view.
