Season chicken with salt and pepper, and dredge the chicken in flour. Heat oil in skillet and sauté chicken until nicely browned on one side (about 3 minutes).
Flip chicken and add garlic and mushrooms. Continue to saute for about 3 minutes, then add the vinegar, broth, bay leaf, and thyme. Cover and simmer over medium-low heat for 10 minutes, turning occasionally.
Remove chicken. Continue to simmer the sauce over medium heat for 7 minutes. Swirl in butter and remove bay leaf. Pour over chicken and serve.