  We investigate the number of holes created by an ``earthworm'' moving on the
two-dimensional integer lattice. The earthworm is modeled by a simple random
walk. At the initial time, all vertices are filled with grains of soil except
for the position of the earthworm. At each step, the earthworm pushes the soil
in the direction of its motion. It leaves a hole (an empty vertex with no grain
of soil) behind it. If there are holes in front of the earthworm (in the
direction of its step), the closest hole is filled with a grain of soil. Thus
the number of holes increases by 1 or remains unchanged at every step. We show
that the number of holes is at least $\mathcal{O}(n^{3/4})$ after $n$ steps.
