Step 1 Heat the oil in a large skillet over medium-high heat. Season the chicken with salt and pepper, then dredge in the flour, shaking off any excess flour.
Step 2 Brown the chicken in the oil, turning once or twice, about 5 minutes. Remove the chicken and set aside. Add the shallots and garlic to the pan and cook until fragrant, about 2 minutes. Add the tomato paste and any remaining flour and cook, stirring, 1 minute.
Step 3Add the mushrooms and broth and bring to a boil. Return the chicken to the pan and reduce the heat to medium-low. Simmer until the chicken is cooked through and the mushrooms are tender, about 15 minutes. Stir in the thyme and cook 1 more minute.