Salt and pepper chicken. Heat 1 teaspoon oil in large nonstick skillet over med-high heat. Add chicken and cook 3 minutes on each side. Transfer chicken to a plate.
Add 1 teaspoon oil to same skillet. Add mushrooms; cook over medium-high heat, stir until mushrooms are browned (4 minutes).
Whisk Marsala, broth, and flour in a small bowl. Pour into skillet with garlic. Cook stirring constantly until mixture bubbles and thickens about one minutes. Return chicken to skillet, coat with sauce and sprinkle with thyme. Cook 5 minutes more.