Begin by preheating your oven to 375°F (190°C).
In a spacious skillet, warm a small amount of olive oil over medium heat.
Introduce the onion, celery, and garlic, sautéing them until they become tender, which should take approximately 5 minutes.
Incorporate chicken broth, salt, pepper, sage, and thyme into the skillet, stirring thoroughly to ensure a well-mixed combination.
In a large bowl, merge the cubed bread with the sautéed mixture.
Add the melted butter and heavy cream, mixing until the bread is uniformly coated.
Place the chicken breasts in a baking dish and generously top them with the prepared dressing.
Encase the dish in aluminum foil and place it in the oven to bake for 35 minutes.
After this time, remove the foil and continue baking for an additional 10 minutes, or until the chicken is thoroughly cooked and the dressing achieves a golden brown color.
Serve while hot and savor the dish.