Maybe something like Fluidframes / Moveanything could do it.
But if I dragged the frame out somewhere so undocking it from the chat I was able to toggle its visibility with
Code:
/script ChatFrame2:Hide()
/script ChatFrame2:Show()
Assuming it is ChatFrame2 which could vary depending on what others you have opened/created.
Simply doing this while the frame was docked in the chat did not seem to work, but it did just fine once dragged out.
On a sidenote - i'm slowly working on a UI which will implement this concept, to toggle the visibility of chat frames, minimap etc through some buttons, maybe simple LDB broker launchers.
/framestack - to toggle a display indicating the frames under the mouse.
Should allow you to figure out which chat frame is which.
Repeat the command to turn it off.