Stir cranberry juice, cranberries, ginger and garlic in large bowl until blended. Add chicken, cover, and marinate in refrigerator 1 to 2 hours. Remove chicken from marinade and season with salt and pepper. Reserve marinade.
Melt butter in medium saucepan. Add shallots and saute over medium heat until transparent. Add reserved marinade and bring to a boil, uncovered. Decrease heat to low and simmer 15 minutes, stirring occasionally, until reduced in half. Add carrots last 5 minutes of cooking.
Grill chicken over medium-high heat 4 to 6 minutes per side until juices run clear when pierced with a fork or chicken reaches internal temperature of 165 F.
Place grilled chicken on a large serving platter, drizzle with reduced marinade, and garnish with chopped chives. Serve with seasonal vegetables and a whole grain side dish like brown rice or quinoa.