Put the chicken breast fillets, onion, celery, carrot, black peppercorns, lemon zest and bunch of dill in a large saucepan. Add the water. Bring to the boil over a medium heat, skimming off any foam that comes to the surface. Reduce the heat and half cover the pan with a lid, so the water just bubbles gently. Simmer for 15 minutes or until the chicken is cooked through.
Remove the chicken from the pan with a slotted spoon and set aside. Strain the stock through a sieve into a clean pan, discarding the vegetables and flavourings.
Reheat the stock until boiling, then stir in the rice. Simmer gently for 8–10 minutes or until the rice is almost tender. Meanwhile, cut or tear the chicken into thin shreds, and mix the lemon juice with the beaten eggs.
Add the shredded chicken to the soup. Heat over a medium heat until the soup almost starts to boil again. Remove the pan from the heat and pour in the lemon juice mixture, stirring constantly. Serve seasoned with salt and pepper to taste and garnished with sprigs of dill.