Gather all of your ingredients and chop the vegetables.
Melt the butter in a large pot over medium heat. Once the butter is completely melted, add the celery and carrots. Cook them until tender, seasoning with salt and pepper. Add the garlic later and cook for about 30 seconds.
Sprinkle the flour over all the vegetables as evenly as possible and stir for a few seconds until the vegetables look coated. Then add the thyme, bay leaves, potatoes, chicken, and chicken broth.
Bring the soup to a light boil and simmer until the chicken is cooked through, and the potatoes can easily be speared with a fork. Then taste and adjust salt, pepper, and other seasonings to your liking.
Cut off the heat, and remove the chicken pieces to a plate or bowl. Shred the chicken meat with two forks and then returned it to the soup. Stir until everything is evenly distributed.
Ladle the stew into bowls and then garnish with parsley.