In a large stock pot over medium heat, add 2 quarts chicken broth, chicken, carrots, celery, mushrooms, garlic, onions, salt, pepper, Worcestershire sauce, tarragon, thyme and bay leaf. Cover with lid and cook for 30 minutes.
In a sauce pan over medium-high heat, add rice and remaining chicken broth. Bring to a rolling boil. Cover with lid, reduce heat to medium and let cook for 20 minutes.
Remove chicken from stock pot and chop up. Return to pot and let continue to simmer until rice is done cooking.
Add a portion of cooked rice to a bowl and ladle soup over top. *Be sure not to serve the Bay Leaf