Does Fountain support chapters?

Yes, Fountain supports chapters. When publishing an episode in Fountain, have two options:

Use Fountain’s auto-generated chapters

Fountain will start generating chapters for your episode as soon as you've uploaded your audio or video. You can also adjust the start time, title, link and artwork for each chapter. After publishing the episode, the chapters will be included in your feed and will be available to listeners in supporting apps. 

Upload your own chapters

If you already have a chapters from a third-party service, you have the option to upload a JSON file. Just check the box next to "I want to upload my own chapters" and choose the file. You are also able to edit your chapters after uploading the file.