Please read the Fetish
FAQ befor posting questions. It covers stuff like chat window stealthing, Head button and showing the Personabar.
Edit: My apologise... the FAQ instructions for disabeling chat input stealthing were in error and have been corrected.
BrantBear, it sounds like you have a bugged server_character_settings.ini file. This used to be a very common problem on SOE's end that usually requires trashing your existing settings file and redoing your window layout for that toon. The symptoms are windows (chat in particular) that refuse to save possition and/or reapear on login.
Sometimes you can force the window to be updated by doing the following...
1) Manually move the window it in game
2) Wait 2 min for the client to save your settings
3) Close the window if you want it gone
4) Wait another 2 min
5) Try relogging. If it reappears, you probably need to trash your settings file.