Preheat oven to 450° F. Place carrots, potatoes, corn, and onion in large bowl. Generously spray with cooking spray; season with 1/2 teaspoon of salt and 1/4 teaspoon black pepper. Toss to coat. Spray 13x9 baking dish with cooking spray. Pour vegetables evenly in bottom of baking dish.
Place chicken over vegetables; lightly spray with cooking spray. Season with smoked paprika and remaining salt and pepper. Squeeze lime juice over chicken and vegetables. Place lime halves, garlic, and rosemary into cavity of chicken.
Bake 50 to 55 minutes or until chicken is brown and thermometer inserted into thigh reaches 180° F. Let chicken rest 20 minutes before serving.
COOK'S TIPS: A 6-quart Dutch oven, with ovenproof handles, may be used for a rustic presentation.
Smoked paprika can be found in your local supermarket in the spice aisle. The smoky flavor provides a delicious taste twist.