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Preheat oven to 350F degrees. Spray a 9 x 13 baking dish with nonstick cooking spray.
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In a small skillet over medium heat, melt the butter and add chopped onion and celery.
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Cook for about 8-10 minutes (until veggies are soft). Season with salt and pepper.
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Pour the butter and veggie mixture into your prepared baking dish.
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Add the chicken in a layer on top of the vegetables.
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In a small bowl, combine self-rising flour with milk.
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Pour this mixture over chicken (do not stir mixture).
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In another small bowl combine the chicken broth with the cream of chicken soup. Season with ab it more salt and pepper.
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Pour this mixture over the chicken. Do not mix the layers.
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Then bake for about 45-50 minutes or until the casserole is set.