In a small bowl, combine thyme, salt, and pepper. Rub mixture evenly on chicken quarters.
In a large bowl, place flour. Dredge chicken in flour, shaking to remove excess.
In a large dutch oven over medium heat, heat oil. Brown chicken, in batches, on all sides. Remove from pan to a plate, and set aside.
Add onion, carrot, and garlic to the Dutch oven and cook until vegetables are tender approximately 5 minutes. Add chicken broth and bring to boil.
Return chicken and plate juices to pot and bring mixture to a simmer. Simmer until chicken is fork-tender and falling off the bone, approximately 1 hour. Add peas, and cook until tender 5 minutes for frozen. Taste and adjust seasonings, if desired. Serve over rice.