Whisk together the oil, vinegar, basil, onion, salt, peppercorns, and garlic in a bowl. Transfer the marinade to a gallon-sized sealable plastic bag with the chicken and shake to combine. Refrigerate for at least 3 hours and up to 12 hours.
When ready to cook, build a charcoal fire or preheat gas grill.
Remove chicken from the marinade. Grill the chicken, turning once, until browned and just cooked through, about 4 minutes per side. Transfer the chicken to a platter and garnish with the basil sprigs.