Preheat grill to medium.
Purée onion, herbs, 2 Tbsp oil, lemon juice and a bit of salt and pepper in a food processor.
Spread onion-herb mixture over chicken and grill about 15 minutes on each side, rotating 90° on each side halfway through.
Note: Frenched chicken breasts have the cleaned wing bone attached, and are often known as chicken supremes. You can ask your butcher to prepare this for you, or to prepare at home, run a boning knife around the middle of the drumette portion of the wing to remove excess meat (cleaning the bone).