Actually, apologies, this doesn't get returned directly by the Chooser, but this is possible to get now depending on the link type setting you're using with the Chooser. That is, if you use the "preview" link type, you can then pass the link to /metadata/link to get the metadata, including path:
"in_dropbox: Returns true if the file or folder is in the authenticated user's Dropbox. If no access token is passed, then this will always return false.
path: Returns the path to the file or folder relative to the shared link's root. If the in_dropbox value is true and the shared link points to a file or folder within the authenticated user's Dropbox, it returns the same path that would be returned by the /metadata endpoint. If the request is made without an authenticated user or the shared link is not in the authenticated user's Dropbox, this will always return null."
I hesitate to say this, because I am a terrible, terrible hobbyist programmer, but, I wrote up a tutorial on this.
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