But what do you do when you can't split a large user story into a small enough chunk that still delivers value?
This XP article is useful - but one of the most useful tools that sometimes gets forgotten is to remember the law of diminishing returns. Sometimes wrapped up in the guise of a single requirement, are multiple smaller/ less valuable features. Look for the portion that's going to give you the most bang for your buck.
Break everything else out into other stories.
It's like giving your Product Owner an itemized quote rather than a all-inclusive one, and all of a sudden they have the ability to prioritize better.
You'll be surprised as to what they'll "live with" when they can see how much it costs.