To make sauce, combine lemon juice and garlic in a bowl. Add oil in a thin stream, whisking continuously, until sauce thickens slightly. Stir in herbs and season to taste. Place chicken in a shallow dish and brush with one-third of sauce. Cover and refrigerate for 30 minutes to marinate.
Preheat barbecue on medium. Fold a sheet of foil in half to form a rectangle. Place tomatoes, onion and oregano in centre of foil and drizzle with oil. Wrap up to form a parcel. Cook for 15 minutes, until onion is soft. When ready to serve, open to let steam escape.
Meanwhile, cook chicken on open grill for 4 minutes each side, until browned and cooked through. Serve chicken with remaining green sauce, tomatoes and crusty bread.