Sprinkle each chicken breast liberally with salt and pepper. Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat. Cook the chicken until browned, 4 to 6 minutes per side. Transfer to a plate and cover with foil.
Add the remaining 2 tablespoons oil to the same skillet over medium-high heat and saute the mushrooms until softened, 2 minutes. Add the wine and cook 1 minute before adding the beef broth and thyme. Bring the sauce to a simmer and let reduce by three-quarters, about 15 minutes. The sauce should have thickened and turned a rich dark brown. Just as the sauce is almost done, return the chicken to the pan and finish cooking through to 165 degrees F, about 5 minutes. Season with salt and pepper.
Serve the chicken with the mushrooms and Madeira sauce and garnish with fresh thyme.
Per serving: Calories 280; Total Fat 14 grams; Saturated Fat 2 grams; Protein 29 grams; Total Carbohydrate 4 grams; Sugar: 3 grams; Fiber 0 grams; Cholesterol 76 milligrams; Sodium 296 milligrams
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