Place the chicken broth in a 4 quart casserole and bring to the boil. Add the carrots and celery and simmer for 10 minutes. Mean put he butter in a saute pan and begin to cook the shallots over medium heat. Add the mushrooms to the pan and cook over high heat for 5 minutes .
Add the cream to the pot over broth and vegetables and then add the Sauteed mushrooms to the pot. Simmer this for 5 minutes before adding the chicken and continuing to cook for 20 minutes. Add the tarragon and place into single serving crocks or bowls and top each one with a biscuit.