- Place the chicken in a large pot and cover with the chicken broth. Bring to a boil and simmer for 5 minutes.
- Add the potatoes, carrots, celery and leek to the pot. Cook for another 15 minutes or until the vegetables are tender and the chicken is cooked through, skimming the surface of the soup, as needed.
- Using a slotted spoon, remove the vegetables and chicken and set aside separately. Let the chicken cool, then cut into large dice.
- In a sieve set over a large bowl, strain the broth. Return the broth to the pot and bring to a boil.
- In a small bowl, combine the butter and flour. Whisk the beurre manié into the broth. Simmer for 10 minutes. Add the cream and cook for 2 more minutes. Return the chicken and vegetables to the pot. Reheat for 2 minutes. Adjust the seasoning.
- Serve the soup in bowls. Garnish with the tarragon leaves and serve with a slice of fresh bread, if desired.