Place carrots, celery, 3 cloves of garlic, sliced onions, and potatoes in a 6-qt. slow cooker; sprinkle with ½ teaspoon salt and ¼ teaspoon pepper.
Place lemon halves, onion halves and 3 garlic cloves in the chicken cavity.
Tuck wings under the chicken and tie drumsticks together. Place the chicken over the vegetables in the slow-cooker, breast side up.
Mix together rosemary, lemon juice, oil, paprika and remaining salt in small bowl; rub all over the chicken.
Cook, covered, on low until a thermometer inserted in thigh reads at least 170° and vegetables are tender, 6-8 hours.
Let stand 15 minutes before carving. Serve with the vegetables.