Place chicken breasts in a large freezer bag or between two sheets of plastic wrap and pound with a meat mallet, rolling pin, or heavy can to an even thickness of 1/2–3/4 inch.
In a bowl or large freezer bag, whisk together olive oil, lemon juice, lemon zest, minced garlic, balsamic vinegar, Dijon mustard, dried oregano, salt, pepper, dried basil, dried thyme, onion powder, paprika, sugar, and red pepper flakes until combined.
Add the chicken to the marinade, seal, and turn to coat. Marinate in the refrigerator for up to 4 hours.
When ready to cook, remove chicken from the refrigerator and let it sit at room temperature for 15–30 minutes.
To grill: preheat the grill to 400°F, clean and oil the grates, then grill chicken undisturbed 5–7 minutes per side until an instant-read thermometer reaches 160°F; let rest 5 minutes to reach 165°F before slicing. Serve with lemon wedges and parsley if desired.
To pan-sear: heat 1 tablespoon olive oil in a large skillet over medium-high heat until very hot. Add chicken and cook undisturbed 3–4 minutes until deeply golden, flip, cover, reduce heat to medium, and cook 5–7 minutes more until thermometer reads 160°F. Rest 5 minutes to reach 165°F before slicing.
To bake: preheat oven to 425°F and lightly grease a baking dish. Drain chicken from the marinade, place in the dish, and bake uncovered 16–18 minutes for 1/2-inch-thick breasts or longer for thicker pieces until internal temperature is 160°F. Rest 5 minutes to reach 165°F before slicing.