  The sensitivity of the random field Ising model to small random perturbations
of the quenched disorder is studied via exact ground states obtained with a
maximum-flow algorithm. In one and two space dimensions we find a mild form of
chaos, meaning that the overlap of the old, unperturbed ground state and the
new one is smaller than one, but extensive. In three dimensions the
rearrangements are marginal (concentrated in the well defined domain walls).
Implications for finite temperature variations and experiments are discussed.
