In a large pot, combine the chicken thighs, onion, dill, celery, bay leaves, peppercorns, allspice, and water. Season generously with salt and pepper.
Bring to a boil over high heat.
Reduce the heat to low, cover the pot with the lid slightly ajar, and simmer for 1 hour 15 minutes.
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.
