  We present a continuous time random walk model for the scale-invariant
transport found in a self-organized critical rice pile [Christensen et al.,
Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that
the dynamics of the experiment can be explained in terms of L\'evy flights for
the grains and a long-tailed distribution of trapping times. Scaling relations
for the exponents of these distributions are obtained. The predicted
microscopic behavior is confirmed by means of a cellular automaton model.
