Preheat oven to 450 degrees. Bake bread in a single layer until dry, 5 to 7 minutes. Transfer to a large bowl. In a medium skillet, melt butter over medium. Add onion, garlic, and celery, and cook, stirring occasionally, until translucent, about 5 minutes. Add thyme, and cook until fragrant, about 1 minute. Stir into bread, then stir in enough broth to make mixture evenly moist but not wet. Season with salt and pepper.
Pat chicken dry. Season inside and out with salt and pepper. Stuff cavity, tie legs together, and tuck wings underneath. Roast chicken until an instant-read thermometer inserted into thickest part of the thigh registers 165 degrees, about 1 hour (tent exposed stuffing with foil if overbrowning). Let rest 10 minutes before serving.