  In this letter we consider the fluctuation induced force exerted between two
plates separated by a distance $L$ in a fluid with a temperature gradient. We
predict that, for a range of distances $L$, this non-equilibrium force is
anomalously large compared to other Casimir forces. The physical reason is that
correlations in a non-equilibrium fluid are generally of longer range than
other correlations, even than those near an equilibrium critical point. This
giant Casimir force is related to a divergent Burnett coefficient that
characterizes an Onsager cross effect between the pressure and the temperature
gradient. The predicted Casimir force should be detectable with currently
available experimental techniques.
