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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.
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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.