Cut a piece of chicken wire that runs the length of the gap under your fence. Make the piece slightly larger than twice the width of the gap.
Fold the chicken wire in half; it's now just slightly wider than your gap. Jam the folded chicken wire into the gap with the spine facing down, so the bottom of the fence sits between the open fold.
Lay heavy rocks on both sides of the chicken wire. This will keep the wire firmly in place and discourage digging. Make sure that your top level of stones covers the sharp edge of the chicken wire so that your dog's paws do not get caught in it.
Cover the rocks with a layer of soil. Pat the soil down with the shovel to compact it and make it even.
Plant shrubs along the fenceline to further discourage digging.