Combine the spinach, pine nuts, lemon juice, and lemon peel in a processor. Lightly pulse. With the machine running, gradually add 1/3 cup of the oil, blending until the mixture is creamy. Add salt and pulse. Put half of the pesto into ice cube trays and store in the freezer for future use.
Transfer the rest of the spinach mixture to a medium bowl. Stir in the Parmesan. Season the pesto with salt and pepper, to taste.
Spread the pesto over each piece of chicken and serve.