Prepare the chimichurri. Finely chop the parsley, green onions, oregano, garlic, and chili pepper (if using). Place everything in a bowl.
Mix the sauce. Add the oil, white vinegar, salt, and black pepper. Stir until all the ingredients are evenly combined.
Transfer the chimichurri to a heatproof glass jar. Once your coals are fully lit, place a small piece of hot charcoal into the jar and immediately close the lid for about 2 to 3 minutes. The smoke will stay trapped inside, giving the chimichurri a wonderful smoky aroma. Carefully remove the charcoal afterward and close the lid.
Score and season the chicken. Pat the chicken breasts dry with a paper towel. Using a sharp knife, make 2 to 3 shallow diagonal cuts (scoring) across the thickest part of each breast. Season both sides generously with the kosher salt and black pepper.
Grill the chicken. Grill over medium heat for about 9 to 11 minutes per side, or until the thickest part reaches 165°F (74°C). Cooking over medium heat keeps the chicken juicy and tender.
Serve. Transfer the chicken to a serving platter and generously spoon the chimichurri over the top. Serve immediately with extra chimichurri on the side.