Cut the chicken legs to separate the thighs and drumsticks. Rince the chicken and pat dry with paper towels. Remove as much fat as possible. Sprinkle with salt and pepper.
Heat the oil over medium-high heat in a large Dutch oven. Use tongs to add the chicken pieces in a single layer; do not crowd. Cook until browned all over, about 5 minutes per side. Transfer the cooked pieces to a platter and set aside. Repeat until all the chicken is browned.
Add the onion, mushrooms, and garlic to the Dutch oven and saute until the mushrooms give up their juice, about 8 minutes.
Return the chicken to the Dutch oven. Add the tomatoes, broth, thyme, and bay leaf. Cover and simmer until the chicken is tender, 25 to 35 minutes.