Step 1Heat 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 2Brown 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.