Melt the butter in a large pot, and cook the onion, celery, carrot, potatoes, and squash 5 minutes, or until lightly browned. Pour in enough of the chicken stock to cover vegetables. Bring to a boil. Reduce heat to low, cover pot, and simmer 40 minutes, or until all vegetables are tender.
Transfer the soup to a blender, and blend until smooth. Return to pot, and mix in any remaining stock to attain desired consistency. Season with salt and pepper.