Prepare marinade: In a bowl, whisk together zest, juice, oil, garlic, salt, pepper and sugar until combined.
Put chicken in a Ziploc bag and pour marinade over chicken. Shake to coat and put in the refrigerator to marinate until ready to use (at least 15 minutes to overnight).
Prepare sauce: In a blender, add parsley, oil, shallot, vinegar, garlic, salt, pepper, and juice. Blend until smooth (about 1 minute).
Preheat grill. Place chicken on grill (discard marinade) and cook chicken on 4 to 5 minutes per side, or until thoroughly cooked.
Serve chicken with a drizzle of sauce and garnish as desired. (Store any leftover marinade in the refrigerator).
Recipe by Alida's Kitchen at https://www.alidaskitchen.com/2012/08/15/grilled-lemon-chicken-with-parsley-sauce/