In a large pot combine chicken, water, large onion, celery with leaves, fresh parsley, peppercorns, stock cubes, bay leaf, celery seed, thyme and 1 teaspoon salt. Bring to a boil, then reduce heat, cover and simmer four hours.
Strain stock, reserving chicken, and refrigerate for 30 minutes.
Skim fat from top of stock. Remove skin and bones from chicken and cut meat into bite-size pieces. Return stock and chicken to pot and stir in carrots, 1/2 cup sliced celery, 1/4 cup minced onion, dried parsley, 1 teaspoon salt, pepper and rice. Bring to a boil, then reduce heat and simmer 30 minutes.