overflow:hidden seems to work, but it feels wrong. You'll almost certainly have to restore overflow:scroll when you want the box to be available to the user. I'd be more inclined to use the visibility property to toggle the element in and out.
I looked at it yesterday but didn't post because I am not js/Ajax fluent, don't use a Chrome browser to check against.
..but in simple terms of css, the scrollbar comes from assigning a height of 200px to the textarea element. A width:0 wouldn't change that. If you remove the height attribute from the textarea css, the scrollbar disappears in FF. If you need that height for positioning, you might try to contain the form to a div with the 200px height setting.