Gather the ingredients.
Heat oil in a large skillet over medium-high. Season chicken with ¼ teaspoon each salt and pepper, and add to the pan. Cook until browned, turning, about 8 minutes in all. Remove. Pour off all but 1 tablespoon fat from the pan.
Add the butter to the pan and reduce heat to medium-low. Add onion and cook, stirring occasionally, until translucent, about 5 minutes. Increase the heat to medium-high. Add the mushrooms, garlic, and ¼ teaspoon salt. Cook, stirring frequently, until the vegetables are browned, about 5 minutes.
Add the flour and cook, stirring, for 30 seconds. Stir in the vermouth and bring back to a simmer.
Stir in the broth, tomatoes, thyme, and the remaining ½ teaspoon salt.
Add the chicken and any accumulated juices. Reduce the heat; simmer, covered, until the chicken is done, about 10 minutes.
Stir in the parsley and the remaining ¼ teaspoon pepper.
