In a 6-quart Dutch oven heat 1 tablespoon of the butter over medium heat until melted. Add the chicken and cook just until browned on the outside, stirring occasionally. Remove from Dutch oven, set aside.
In the same Dutch oven, heat remaining 1 tablespoon butter over medium heat until melted. Add onion, celery, and carrots; cook about 5 minutes or until tender, stirring occasionally. Add broth. Bring to boiling; reduce heat. Simmer, covered, for 10 minutes. Stir in potatoes. Simmer, covered, for 10 minutes more or until potatoes are tender. Stir in reserved chicken.
In a small bowl combine the flour and 1/4 cup softened butter to make a smooth paste. Stir flour mixture into broth mixture. Cook and stir until thickened and bubbly. Cook and stir for 1 minute more. Add half-and-half. Cook and stir over medium heat until heated through. Season to taste with salt and pepper. Top each serving with bacon.