Gather all ingredients.
Sprinkle the chicken evenly with ½ teaspoon salt and ½ teaspoon pepper. Place flour in a shallow dish; dredge chicken lightly in flour, shaking off excess. Discard any remaining flour.
Heat 2 tablespoons butter in a large skillet over medium-high. Cook 3 to 4 minutes on each side until golden brown and cooked through. If needed, brown the chicken in 2 batches. Transfer the chicken to a plate and keep warm.
Melt 1 tablespoon butter in pan and add mushrooms, onion, and remaining ¼ teaspoon salt and pepper. Cook until mushrooms are browned and have released their liquid, about 6-7 minutes. Add the garlic and thyme and cook 1-2 minutes longer, until fragrant.
Stir in chicken broth and vinegar. Bring to a simmer and cook until liquid has reduced by half, about 5-8 minutes. Whisk in remaining 3 tablespoons butter until melted and smooth. Add chicken back to sauce and cook for 3-5 minutes until chicken is coated and warmed through. Sprinkle with additional thyme, if desired, and serve immediately.
