1. Place each chicken breast in a large zip-lock bag or on a cutting board and pound to an even thickness of about ½ inch, or slice horizontally into thin cutlets about ¼ inch thick.
2. In a bowl or large zip-lock bag, combine olive oil, garlic, thyme, oregano (or Italian herbs), salt, pepper, lemon zest (or vinegar), and optional brown sugar. Mix well.
3. Add the chicken breasts to the marinade, massage to coat evenly, then refrigerate for at least 30 minutes to 4 hours or overnight.
4. Preheat the grill to high heat. Clean and oil grill grates thoroughly.
5. Place chicken on the hot grill, cover, and cook for 2 to 6 minutes per side, turning once and basting occasionally with reserved marinade if desired. Ensure the internal temperature reaches 165°F.
6. Transfer the chicken to a platter and let it rest for 3 to 5 minutes before slicing.