In a bowl combine Cream Soup Cans, Onion Soup Mix, Dried Thyme, Pepper, and Dried Tarragon in a large bowl.
Add carrots and onions to the bowl and mix.
Put chicken into slow cooker and pour mixture over the top. Use a rubber scraper to get it all off the sides and into the slow cooker.
Let mixture and chicken cook for 4-5 hours on high.
Mix corn starch into chicken broth and stir it intoslow cooker mixture.
Cover back up and cook for 30 min.
Serve over rice.