Prepare the Marinade - In a medium bowl, vigorously whisk together olive oil, water, lemon juice, mustard, soy sauce, honey, garlic, parsley, salt, lemon zest, black pepper, and paprika. Reserve ¼ cup for basting.
Marinate the Chicken - Add the chicken to a baking dish or large resealable plastic bag. Pour the marinade over, turn to coat, cover, and refrigerate. Press out any excess air if using a plastic bag. Marinate for a minimum of 30 minutes and up to 60 minutes.
Preheat the Grill - Preheat the grill over medium-high heat between 375 to 400ºF (191 to 204ºC). Keep one burner off for indirect heat cooking. Clean and carefully grease the grates with the oil.
Grill the Chicken - Shake off excess marinade from the chicken. Lightly dry the surface with a paper towel. Place the meat skin-side down on the grill. Close the lid and cook for 5 minutes. Flip and baste with the reserved marinade. Cook covered for about 5 minutes. Repeat flipping and basting with the remaining marinade every 2 to 3 minutes.Cook until the internal temperature reaches about 165 to 170ºF (74 to 77ºC) on a meat thermometer, about 25 to 30 minutes. If browning too quickly, move the pieces to the indirect heat side of the grill to finish.
To Serve - Cover the chicken with foil to keep warm. Rest for 5 minutes before serving.
Notes
Servings: About 6 pieces, varies by brand
Marinade: Makes about 2/3 cups
Storing: Store grilled chicken in an airtight container in the refrigerator for up to 5 days.
Reheating: Cover and microwave the chicken on high heat in 15 to 30-second increments until hot.
Marinating Ahead of Time: Chicken can be marinated for up to 24 hours, but wait to add the lemon juice (acid) until the last 30 to 60 minutes.
Using Boneless Thighs: Check for doneness after the first 10 minutes of cooking. Less time will be needed.
Make it Paleo: Use pure maple syrup instead of honey. Use coconut aminos instead of soy sauce.
Make it Gluten-Free: Substitute soy sauce with gluten-free tamari or coconut aminos.
Make it Keto: Use coconut aminos instead of soy sauce. Omit honey or use erythritol.