Is there a way to take FCPX chapter markers to Encore?

Not in my experience.

You would need to export as .mov then add the chapters again in encore.

I have read about a convoluted method involving exporting a XML file with chapter markers which then imports into Encore as regular markers which then have to be individually converted into Encore chapter markers. Never tried this as I almost never use Encore except for BluRay menu authoring and nobody has asked me for that in a long time.