Oh ok. So you have this right now (your FB icon)
<a href="https://www.facebook.com/groups/xboxlink/" target="_blank"><img src="http://img827.imageshack.us/img827/8018/oie161143538fl0novm.jpg"></a>
Put that right before this code:
Then, change your CSS for your FB icon to this:
Note that I took out a lot of the CSS. They were unnecessary.
Try that first. The chat and FB icon will now be next to each other and moving together, but you'll need to mess around with the position a bit to get them looking the way you want them to look.