There's currently no ability to export just a single chapter Atticus, however, you can export a full-sized PDF of a single chapter with the work around listed below:
To view a full-sized PDF of a chapter or save the chapter, you’ll want to open your book in Atticus and click on the chapter you'd like to view:
Click the preview option at the bottom of the right hand side bar and change the preview form the default iPad view to Print
Give it a moment to render your book then click on the page in the preview
This will open up that chapter alone in a PDF in your browser, so you can view the full size PDF of this chapter there or save it to your computer.
You can also duplicate a book from the Atticus home screen by clicking the three dots near the title and selecting duplicate. Then, delete any content from this version that you don't want to appear in the excerpt and export this file.