In a large pot, combine the chicken thighs, onion, dill, celery, bay leaves, peppercorns, allspice, and water. Season generously and bring to a boil.
Remove chicken thighs from the pot and set aside. Strain the broth through a fine mesh strainer into another pot. Discard solids.
Once chicken is cool enough to handle, remove meat from bones and shred into bite-sized pieces. Return shredded chicken to broth. Taste and adjust seasoning as needed.
Serve hot, garnished with fresh dill if desired.