Preheat oven to 300F.
Sprinkle chicken pieces with salt and pepper. In a Dutch oven over medium heat place 1 Tbsp. of olive oil and brown the chicken on both sides until it is about ¾ of the way cooked.
Remove chicken from Dutch oven and place in a 13"x9" oven safe glass dish along with the carrots. Sprinkle with tarragon and set in oven uncovered for about 35 minutes.
Scrape out the Dutch oven and toss out the scrapings.
Add the remaining tablespoon of olive oil to the Dutch oven and saute the shallots and the celery until shallots begin to brown slightly.
Add the stock, bay leaves and the wine and bring to a boil. Let it boil for about 2 minutes and turn heat down to medium. Stir in the tomato paste. Reduce the sauce to about 2 cups.
Remove 1 cup of the juice and set aside.The other cup will be used to baste the chicken that is cooking in the oven. Baste every 5-10 minutes.
For the cream sauce: Place cream in a small saucepan on medium heat. Slowly add the reserved 1 cup of juice stirring constantly. Reduce the sauce until it coats the back of a spoon(nappe consistency).
Transfer the chicken from glass dish back to the Dutch oven to serve.
Pour cream sauce over chicken.