Of course, it all depends upon definitions... This article claims that to go "all in" on Advanced Squad Leader, you need to drop $3200. But, presumably you meant "a single box"?
If you use EBay as a way to track prices, as of today, there's a $1K price on Advanced Civilization, and the second highest at $600 is ... Queen's Gambit. Those are asking prices, not sale prices.
BoardGame Geek's list of most expensive games available for purchase today, none of them are AH, but based on the lack of hits on EBay, one can assume it's not a particularly liquid market.
Finally, my original answer to this question, quoted this article to give answer of: "Star Wars: The Queen's Gambit"
Star Wars: The Queen’s Gambit: Play as either the trade federation or
the Naboo as you reenact the four-fold climax of Star Wars: The
Why it’s rare: It’s great, highly complex, and happens to come with
155 individual pieces, a 3D Theed palace, 16 dice, and 180 cards. Sure
it was released in the comparatively recent year 2000, but prying one
of these suckers from the hands of another Star Wars fan will still