Place carrots, celery, and potatoes into crock pot, and sprinkle with 1/4 teaspoon salt and pepper.
Place lemon halves and garlic into chicken cavity.
Tuck wings under chicken, and tie drumsticks together.
Place chicken over vegetables, breast side up.
Mix together rosemary, lemon juice, olive oil, paprika, and remaining salt in a small bowl, and rub over chicken.
Cover crock pot, and cook on low for 6-8 hours until chicken is cooked through and vegetables are tender.
Remove chicken from crock pot, and let stand 15 minutes before serving.