Slice the zucchini lengthwise, into thin slices using a mandolin.
Roll up a slice of zucchini and place it into the cupcake baking sheet, use 2 slices to fill the cups if necessary. Press the slices of zucchini down as much as possible, until you reach the bottom.
Use a couple of slices to cut small squares of the zucchini, and add the zucchini squares to the bottom of the cups. Add the small squares of chicken on top of the zucchini squares. Crack an egg in each cup, sprinkle the mozzarella over the cups. Bake for 20 minutes.
Let the zucchini egg cups cool for a couple of minutes before removing them.