Mix cider vinegar, mustard, garlic, lime juice, lemon juice, brown sugar, salt, and pepper together in a large glass or ceramic bowl.
Whisk in olive oil.
Add chicken and toss evenly to coat.
Cover, and marinate in the refrigerator for 8 hours to overnight.
Preheat an outdoor grill for high heat.
Lightly oil the grill grate.
Place chicken on the preheated grill, and cook 6 to 8 minutes per side, until juices run clear.
Discard any remaining marinade.
