Bring chicken broth, onion, carrot, celery, bay leaf and salt to a simmer. Add chicken thighs, cover and poach (gently simmer over low heat) for 1 hour. Remove chicken thighs, let cool slightly and pull or cut chicken into strips. Set aside. Strain soup and return to boil. Add rice and gently simmer for 20 minutes, then add chicken back to soup for another 5 minutes.
Whisk yolks in lemon juice. Add a cup of the hot soup, very slowly, whisking while you pour it inches Add another cup in the same manner. Take soup off the heat and add egg mixture into it. Sprinkle with parsley, season with salt and pepper and serve.