Pour only enough olive oil (about 1 1/2 tablespoons) on a cookie sheet to prevent the chicken and the fennel from sticking. Place the chicken breast in a single layer on the sheet pan. Place in the broiler for 7 minutes.
Remove and add the fennel in a single layer and brush both sides with the olive oil. Season fennel slices with salt and pepper on both sides. Squeeze juice of 1 lime over the fennel slices and place under the broiler. Broil for 5 minutes.
Some of the edges may blacken slightly. Remove the fennel from the oven and using tongs or a spatula, and turn over each slice of fennel. Top with the Parmesan. Place back under the broiler for 1 1/2 to 3 minutes, or until cheese starts to brown.
Allow fennel to remain in the pan until ready to serve. Do not refrigerate. This is wonderful served at room temperature. Just before serving, squeeze remaining lime juice over fennel slices.