Stir cranberry juice, cranberries, ginger and garlic in a large bowl until blended. Add chicken, cover and marinate in refrigerator 1 to 2 hours. Remove chicken from marinade, reserve marinade. Salt and pepper chicken to taste.
Melt butter in a medium saucepan. Add shallots and saute over medium heat until transparent. Add reserved marinade, bring to a boil, uncovered. Decrease heat and simmer for 15 minutes, stirring occasionally, until reduced in half. Add carrots last 5 minutes of cooking.
Grill chicken over medium-high heat 4 to 5 minutes per side until juices run clear when pierced with fork or chicken reaches internal temperature of 165 degrees F.
Place three pieces of chicken on each plate; spoon marinade over chicken. Garnish with chives, if desired.
Serve with seasonal vegetables. Makes 4 servings.