In a large bowl, combine the apple cider vinegar, olive oil, garlic, salt, and pepper.
Place the chicken breasts in the marinade and let them sit for at least one hour.
Preheat the grill to medium-high heat.
Remove the chicken breasts from the marinade and place them on the grill.
Cook the chicken for 6-7 minutes per side, or until the chicken is cooked through.
In a small saucepan, combine the honey and remaining marinade. Heat the mixture over medium heat until it begins to simmer.
Brush the glaze on both sides of the chicken breasts and cook for an additional 1-2 minutes per side.
Remove the chicken from the grill and let them rest for 5 minutes before serving.