Clean leeks carefully and trim the roots and green stems. Slice very thin. Clean and slice celery thinly into bite-sized pieces.
Heat olive oil in a large stock pot. Saute the leeks and celery on low heat for 10 minutes, stirring frequently.
Add 1 cup of the chicken stock and bring to a boil. Cook for another 10 minutes.
Peel and dice potatoes. Add potatoes to the pot and the remaining chicken stock. Bring to a boil.
Reduce heat to simmer. Cover the stock pot, leaving the cover ajar just enough to allow some steam to escape. Simmer for 20-30 minutes or until the potatoes are tender.
Serve garnished with parsley or sauteed mushrooms (if desired).