Preheat the oven to 450 degrees F (220 degrees C).

Rub butter over entire chicken; season with thyme, salt, and black pepper. Place carrots inside cavity; tie legs together. Place chicken, breast-side up, in a roasting pan. Lay bacon strips across top of chicken; secure with toothpicks. Sprinkle with paprika. Pour beef broth into the roasting pan; do not pour over bacon.

Bake in the preheated oven for 15 minutes, then reduce the heat to 350 degrees F (175 degrees C). Baste with broth. Bake until an instant-read thermometer inserted into the thickest part of the thigh, near but not touching bone, reads 165 degrees F (74 degrees C), about 1 hour and 15 minutes, basting every 15 minutes with broth.

Remove bacon; discard toothpicks. Bake chicken to brown the skin, 15 minutes more. Transfer to a serving platter; remove ties. The bacon is edible, but it is best to discard the carrots.