Chrome Refreshes On Orientation Change
I disabled the DPI override for Chrome in the App Settings app for Xposed, and the problem went away. 

Now I'll search for a different way to adjust Chrome's DPI.  

Notes: 


This issue did not occur in Chrome 52, the stock version for this ROM
Clearing Chrome app data did not fix the issue


In the end, I set the DPI for the entire phone to match the desired DPI for Chrome, via the ro.sf.lcd_density setting in the file build.prop.  I then changed the DPI of other apps as necessary with Xposed: App Settings.