Place the chicken thighs in the bottom of the slow cooker. Add the celery root, carrots, onion, and garlic on top.
Pour in the chicken broth. Add the salt, black pepper, and bay leaves.
Cover and cook on low for 6 hours until the chicken is tender and the vegetables are soft.
Remove the chicken thighs and shred them with two forks. Return the shredded chicken to the slow cooker.
Stir in the heavy cream and most of the fresh dill. Cook uncovered on high for 15 minutes to warm through.
Remove the bay leaves before serving. Sprinkle the remaining dill over each bowl.