In a large pot combine chicken, water, large onion, celery with leaves, fresh parsley, peppercorns, bouillon, bay leaf, celery seed, thyme and 1 teaspoon salt. Bring to a boil, then reduce heat, cover and simmer 4 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.