How in the world do I punctuate a story within a story within the original story? And it runs for several chapters.
Unless I'm misunderstanding your question, you would punctuate it like anything else. If you're talking about dialogue, then you would punctuate it according to the rules of nested quotes. That is, you would alternate between single quotes and double quotes as the speakers change.
Does it change constantly between both stories or the "second story" goes uninterrupted from beginning to end?
I've had that problem before: a father reading a story to his children. I used double quotes for the real dialogue and single quotes for characters in the book.