Markers in Media Encoder H.264

Hello, I've exported a 90 minute video that contains chapter markers and they export to a ProRes sub master just fine, but when I convert to a h.264 file for delivery, the markers don't show up.

Does anyone have a recommendation for an alternate file format that is as efficient as the h.264 that supports markers, or is there a way to get my markers to show up. I got my file down to a manageable 5 gigs, but when I tried the HDV setting which does support the markers, I can't get the file smaller than 15 gigs.

There must be a solution.

Thank you in advance for your help.

Dan