Heat a grill pan on medium-high heat. Lightly oil the grill pan. Sprinkle the chicken with salt and pepper. Grill the chicken until cooked through, about 5 minutes per side.
Combine the spinach, lemon juice, and lemon peel in a processor. Lightly pulse. With the machine running, gradually add remainder of the olive oil, blending until the mixture is creamy. Add salt and pulse.
Transfer the pesto mixture to a medium bowl. Stir in the parmesan cheese. Season the pesto with salt and pepper, to taste.
Spread the pesto over each piece of chicken and serve.
Note: you can put the pesto mix into ice cube trays and store in the freezer for future use.
There are 362 calories in 1 serving of Grilled Pesto Chicken Breast.