In a small bowl, whisk together maple syrup, whiskey, mustard, garlic, pepper, and salt.
Place chicken breasts in resealable plastic bag and pour half the whiskey mixture over chicken. Add 3 rosemary sprigs. Marinate in refrigerator for 2 hours or overnight. Reserve remaining marinade.
In a small saucepan, place reserved marinade with remaining rosemary sprigs. Bring to a boil over high heat, reduce heat to medium-low and reduce marinade to 1/2 cup and thickened. Discard rosemary sprigs. Set aside.
Preheat grill to medium-high. Brush grill with oil.
Remove chicken breasts from marinade and discard marinade. Grill for 5-6 minutes per side. Brush with glaze during last 2 minutes. Grill until chicken is opaque and juices run clear. Garnish with fresh rosemary.