In a large glass bowl, mix the cider vinegar, mustard, garlic, lime juice, lemon juice, brown sugar, salt and pepper. Whisk in the olive oil. Place chicken in the mixture. Cover and marinate 8 hours, or overnight.
Preheat a barbecue for high heat.
Lightly oil the barbecue grate. Place chicken on the prepared barbecue and cook 6 to 8 minutes per side, until juices run clear. Discard marinade.
The nutrition data for this recipe includes information for the full amount of the marinade ingredients. Depending on marinating time, ingredients, cook time, etc., the actual amount of the marinade consumed will vary.