1. Warm 1/2 tablespoon of oil in a large nonstick skillet over medium-high heat. Season the chicken with salt and pepper; cook about 6 minutes per side until cooked through. Remove to platter; cover with foil.
2. Warm remaining oil in same skillet over medium-high heat. Add mushrooms, leek, and thyme; cook, stirring often, until mushroom liquid evaporates and leek softens, about 6 minutes. Stir in butter, broth, wine (if using), and any juices from the chicken platter; cook 3 minutes or until most of the liquid evaporates.
3. Divide the sauce among 4 plates; top with chicken.