Bring a large saucepan of salted water to a boil. Add chicken, stock cubes, celery, parsley, salt and pepper. Cook for 45 minutes or until chicken is no longer pink inside. Reduce heat to low and continue to simmer.
While chicken is cooking combine the flour, egg, sour cream and chicken stock in a medium bowl. Mix well and roll dough out on a floured surface. Cut into small squares.
In a small bowl mix together cornflour and enough water to form a thin paste; stir into chicken stew.
Drop the dumplings into the boiling chicken stew and continue to simmer for 5 to 10 minutes or until dumplings are light and puffy.