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 an outdoor grill for high heat.
Lightly oil the grill grate. Place chicken on the prepared grill, and cook 6 to 8 minutes per side, until juices run clear. Discard marinade.