I am looking for help finding a UI mod that allows for the customization and movement of both the chat panel and the mouseover tooltip window. I hate having them in the lower left and right portions of the screen, and I would love to be able to move them around.
If you wish to simply relocate the tooltip then Tipsy @ curse will do just that.
There are multiple addons which will replace that tooltip with more customisable features, but in my opinion tend to get too readily suggested when people simply want it moved.
TipTac, Startip, FreebTip being examples.
If you simply want to move the chat then that is there by default, you just drag the tab on the first chatframe.
If it won't move then it is likely locked, which can be resolved by pointing to tab, right-clicking and unchecking "Lock Tab".
Prat is a nice chat addon, although like the person before me said, you don't need an addon to move the chat ui. It allows copy/pasting of urls , copy/pasting of anything in chat (handy for when someone posts a macro in chat) and a lot of other fun stuff too.