Is the Chess.com tab the one on the far left (first one opened) or is it amongst several others?
I can't close my tab

I doesn't seem to matter whether it is the first tab that iv'e opened or not. Either way it won't close.

Try this http://www.chess.com/clear_cookies.html
I've just opened IE8 with 14 different Chess.com and facebook pages on it and wasn't able to replicate what you're experiencing.
Iv'e got a rather strange problem that I wonder if anyone can help me with.
I use internet explorer 8 to access chess.com and at the same time check my facebook page and other sites using multiple tabs. However, no matter how much I try to, I can't close the chess.com tab. Every other tab closes normally but when I try to close the chess.com tab nothing happens. Iv'e also noticed that in my "recently close tabs" list it claims that I have closed the chess.com tab multiple times but it's still here.
This also means that I can't close internet explorer properly, I always have to Cntl-Alt-Delete then "End Task" my way out of it
Can anyone help me with this?