Whisk the olive oil, lemon juice, lemon zest, parsley, sugar, mustard, salt, pepper, and garlic in a small bowl.
Pour half of the lemon chicken marinade along with 2 tablespoons of water into a 1-gallon zip-top bag or baking dish. Set the remaining half of the lemon chicken marinade aside.
Toss the chicken to coat, then press as much air out of the bag (if using) as possible, or cover with plastic wrap (if using a baking dish). Refrigerate for at least 30 minutes, or up to 60 minutes, flipping every 15 minutes.
Grilling Instructions
When ready to grill, heat a gas grill to high. Allow to preheat for 15 minutes. Remove the chicken from the marinade, shake off any excess, and discard any remaining marinade from the bag or dish.
Grill, with the cover down, for 6-9 minutes, then flip, and grill uncovered until the internal temperature reaches 160, about 2-6 additional minutes.
Remove to a cutting board and allow to rest for 5 minutes. Slice against the grain into ½ inch slices, and serve drizzled with remaining marinade.
Notes
I don't recommend marinating the chicken longer than 60 minutes as the acidity from the lemon breaks down the protein, leaving it with a mushy texture.