Place chicken breasts between two sheets of plastic wrap and gently pound with a meat mallet or rolling pin until they are about 3/4 inch thick evenly. This ensures even cooking.
In a medium bowl, whisk together olive oil, lemon juice, garlic, rosemary, thyme, oregano, salt, and pepper until well combined.
Place the pounded chicken in a large zip-top bag or shallow dish. Pour the marinade over, seal, and turn to coat. Refrigerate for at least 30 minutes, or up to 2 hours. Avoid over-marinating as the acid can break down the texture.
Preheat a gas or charcoal grill to medium-high heat (about 400-450°F). Clean and oil the grates thoroughly.
Remove chicken from marinade, letting excess drip off. Place on the hot grill and cook for 6-7 minutes per side, or until the internal temperature reaches 165°F on an instant-read thermometer. Place lemon halves cut-side down on the grill for the last 3 minutes to char.
Transfer chicken to a plate, tent loosely with foil, and let rest for 5 minutes. Slice against the grain and serve with the grilled lemon halves and a sprinkle of parsley.