Preheat grill to medium-high heat. Melt butter in a medium saucepan over medium heat.
Add shallots and garlic; cook 2 minutes, stirring constantly. Stir in bourbon, Dijon mustard, and maple syrup; bring to a boil. Cook 1 minute, stirring occasionally.
Remove from heat.
Sprinkle chicken breast halves evenly with kosher salt and freshly ground black pepper. Arrange chicken on a grill rack coated with cooking spray; baste with half of bourbon mixture. Grill 5 minutes. Turn chicken over; baste with remaining bourbon mixture. Grill 5 minutes or until chicken is done.