You mean move the minimized chat bar FROM the left edge of the window TO the right edge?
Mine is at least always at the left side.
Or are you using any addon which moves it to the right already and you want it at the left again?
Any AddOns that can move the minimized chat bar from the bottom right corner? Haven't found any yet, Azurah and AUI can't move it.
In game there is a little triangle in the bottom left corner of the chat window. If you click it it, it will minimize the whole chat - condenses it into a thin vertical strip that shows friends online, notifications and number of unread mails.