Preheat the oven to 350°F (175°C).
In a large skillet, melt butter. Add onions and apples; sauté until tender. Stir in curry powder; sauté for 1 minute. Mix in flour; cook for 1 minute.
Combine broth and milk; stir into the skillet until well mixed.
Season chicken breasts with salt and pepper; arrange them in a single layer in a 9x13-inch (or larger) baking dish.
Pour the curry sauce over the chicken.
Bake for 45 to 50 minutes until the chicken is cooked through.
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