I have looked into this a bit and the demands made by the Chicago style makes distinctions which are not available in the citation engine which we (and many other reference managers) use. That said, I have put together a style which produces the same results when you edit the metadata in a particular way:
- Set the type to "Book Chapter"
- Leave/set the title field blank
- Use the "Additional fields" button to add the "Custom sub-type" and populate it with the type of book segment (i.e "introduction", "foreword", etc.).
If you do not want items in your library without titles, you can leave the item with a title and simply edit the document-specific version when you cite it (Go to Paperpile --> View all references to edit document-specific copies of papers in your library). Note, however, that if you do this, the citation will no longer be updated with any changes made to the copy in your library.
Here is the style:
chicago-fullnote-bibliography-foreword.csl (50.0 KB)
To add it to your available styles go to the gear in the upper right of the Paperpile tab --> Settings --> Citation Style --> Upload CSL file.