In large bowl mix the cider vinegar, mustard, garlic, lime juice, lemon juice, brown sugar, salt, and pepper. Whisk in olive oil. Place chicken in mixture. Cover, and marinate for 8 hours.
Preheat outdoor grill on high
Lightly oil grill grate. Place chicken on the grill, and cook 6-8 minutes per side until juices run clear. Discard marinade.