It is not possible to output an MP4 with chapters from Premiere Elements.
Chapters are only available on DVDs, Blurays and WebDVDs.
I found a solution and it works well. I ended up using some freeware called Handbrake to create the MPEG-4 files with chapters. The MPEG-4 videos can be played on a Computer, Smartphone, or Tablet.
Step 1: Create your Adobe Premier project with chapter markers
Step 2: Use Adobe Premier to create a DVD ISO folder of your project
Step 3: Use the Handbrake program to create an MPEG-4 file from your DVD ISO folder
You will want the MPEG-4 files to have an extension of .m4v (not .mp4), so that they will play on Apple and other devices. Use the iPad setting in Handbrake which gives you 640x480 output.
Choose Folder d:\Home Movies in DVD iSO Image Folders\1966 Home Movies
Under Preset, choose iPad
Click Start to encode the video
You now have a MPEG-4 version of your video that you can play on your iPad, iPhone, Android, Computer, or other devices.
I did not know that Handbrake could output Chapter Markers. Good info to have, and thank you for posting it.
One caveat, regarding PrE, is that it cannot burn to an Image/ISO file, like Adobe Encore can. Instead, one can chose Burn to Folder, which will create a VIDEO_TS folder with the IFO, BUP and VOB files inside. Then, one can use the great, free burning utility, ImgBurn, to convert that VIDEO_TS folder into an ISO. It is one extra step, but really an easy one.
Thanks for the post on Handbrake,
Thank you for taking the time and trouble--and showing consideration--to post a detailed description of the solution you figured out.
Too many posters get an answer somewhere, and don't bother to share it.
Mahalo nui loa!