Pound the chicken to an equal 3/4-inch thickness. Place the chicken in a large resealable plastic bag after patting it dry with paper towels.
In a blender or food processor, combine lemon peel, lemon juice, garlic, salt, pepper, olive oil, and basil. Pulse for 30 seconds, or until thoroughly combined.
Pour the marinade over the chicken, seal the bag, and turn to fully coat the chicken. Refrigerate for at least 15 minutes and up to overnight.
Preheat the grill to medium-high heat, or about 400°F.
Remove the chicken from the marinade.
Place each chicken piece separately and grill for 4 to 6 minutes per side, or until thoroughly done.
Transfer to a serving plate and top with more basil, if desired.