Preheat the oven to 375°F (190°C).
Season the chicken breasts evenly with salt, black pepper, garlic powder, and dried thyme.
Heat olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 3-4 minutes per side until lightly browned but not fully cooked. Remove chicken from skillet and set aside.
In the same skillet, add chopped onion, chopped celery, and minced garlic. Sauté for 5 minutes until vegetables are softened.
In a large mixing bowl, combine the condensed cream of chicken soup, chicken broth, and sour cream. Stir in the sautéed vegetables.
Place the browned chicken breasts in a 9×13 inch casserole dish. Pour the creamy vegetable mixture evenly over the chicken.
Prepare the dry stuffing mix according to package instructions, substituting melted butter for any oil or butter called for. Spread the prepared stuffing evenly over the top of the casserole.
Drizzle the melted butter over the stuffing layer.
Cover the casserole dish with aluminum foil and bake in the preheated oven for 30 minutes.
Remove the foil and bake for an additional 15 minutes until the stuffing is golden brown and the chicken is cooked through (internal temperature of 165°F / 74°C).
Let the casserole rest for 5 minutes before serving.