Season the chicken thighs with 3/4 teaspoon salt and 1/4 teaspoon pepper. Set aside.

In a 3 to 4-quart pot, melt the butter over medium heat. Add the shallots and cook, stirring occasionally, until fragrant, 2 minutes. Add the celery, 3/4 teaspoon salt, and 1/4 teaspoon pepper, and cook, stirring occasionally, for 2 minutes more. Nestle the seasoned chicken thighs into the celery mixture. Cook for 1 minute on each side.

Add the chicken broth, turn up the heat to medium-high and bring to a boil. Reduce the heat to medium-low and let simmer until the chicken is tender and cooked through, 20 minutes.

Remove the chicken to a plate to cool for 10 minutes.

Meanwhile, stir the xanthan gum into the soup, bring the soup to a low boil and let it bubble, stirring often, for 3 minutes. Lower the heat to medium-low. Stir in the cream, 1 teaspoon salt, and 1/2 teaspoon pepper.

Using your hands or two forks, shred the chicken then return it to the soup. Stir in the dill, then remove the soup from the heat.

Break the spiralized noodles in half lengthwise, scatter them into the soup, and cook, stirring, for 1 minute. Serve.