Maintenance for the week of April 15:
• [COMPLETE] ESO Store and Account System for maintenance – April 16, 8:00AM EDT (12:00 UTC) - 6:00PM EDT (22:00 UTC)
pChat should do this if I remmeber correctly.
You are able to choose the chat tab to copy from in the settings, if you are logged on another toon.
Be sure to login and configure the chat the way you like it to be on all toons first, having pChat enabled!