In a 12-inch nonstick skillet, heat the oil on medium-high.
Add the mushrooms and cook until they are tender and release their liquid, about 5 minutes, stirring occasionally.
Season both sides of the chicken with the thyme, salt, and black pepper.
Push the mushrooms to the outer edge of the skillet. Arrange the chicken in the center and cook until golden, 2 to 3 minutes per side.
Add the marsala wine to the skillet. Simmer for 1 minute, scraping up any browned bits from the bottom of the skillet.
Add 3⁄4 cup beef stock and simmer until the chicken is tender and cooked through, 8 minutes. Transfer the chicken to a plate and keep warm.
In a small bowl, stir the cornstarch into the remaining 1⁄2 cup stock until dissolved and add to the skillet.
Simmer until the sauce thickens, about 1 minute, stirring constantly. Serve the chicken with the sauce.