In a nonstick skillet, heat 1 teaspoon of oil.
In a medium bowl, mix 2 tablespoons of vinegar, the mustard and garlic. Add chicken and turn to coat.
Transfer chicken and marinade to skillet. Sauté chicken until cooked through, about 3 minutes on each side. Transfer chicken to a platter and keep warm.
Heat remaining teaspoon of oil in skillet. Sauté mushrooms for 1 minute. Add broth, thyme and remaining tablespoon of vinegar. Cook, stirring occasionally, until mushrooms are deep brown, about 2 minutes longer.
Serve chicken topped with mushrooms.
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