In a large glass bowl, mix the cider vinegar, mustard, garlic, lime juice, lemon juice, brown sugar, salt, and pepper together.
Whisk in the olive oil.
Place the chicken in the mixture, making sure it is coated all over.
Cover and marinate the chicken in the bowl for at least 8 hours and up to overnight.
Preheat the grill to high heat.
Lightly oil the grill grate.
Place the chicken on the prepared grill and cook until the juices run clear and the chicken reaches 165 degrees F internally, about 6-8 minutes per side.
