  The dark matter halos that surround Milky Way-like galaxies in cosmological
simulations are, to first order, triaxial. Nearly 30 years ago it was predicted
that such triaxial dark matter halos should exhibit steady figure rotation or
tumbling motions for durations of several gigayears. The angular frequency of
figure rotation predicted by cosmological simulations is described by a
log-normal distribution of pattern speed with a median value 0.15hkm/s/kpc (~
0.15h rad/Gyr ~ 9h deg/Gyr) and a width of 0.83km/s/kpc. These pattern speeds
are so small that they have generally been considered both unimportant and
undetectable. In this work we show that even this extremely slow figure
rotation can significantly alter the structure of extended stellar streams
produced by the tidal disruption of satellites in the Milky Way halo. We
simulate the behavior of a Sagittarius-like polar tidal stream in triaxial dark
matter halos with different shapes, when the halos are rotated about the three
principal axes. For pattern speeds typical of cosmological halos we
demonstrate, for the first time, that a Sagittarius-like tidal stream would be
altered to a degree that is detectable even with current observations. This
discovery will potentially allow for a future measurement of figure rotation of
the Milky Way's dark halo, and perhaps enabling the first evidence of this
relatively unexplored prediction of LambdaCDM.
