It turns out there is exactly one: Mayflower Thanksgiving Ale from Mayflower Brewing Company in Plymouth, Massachusetts, appropriately enough. The relatively young brewery (founded in 2007) describes the beer thusly:
Our first seasonal brew! Mayflower Thanksgiving Ale is an inspired blend of two brewing styles: American Strong Ale and English Old Ale. Aged on American white oak, this full-bodied brew warms the soul with hints of caramel, vanilla and spicy nuts.
It’s 8% alcohol by volume and has garnered decent reviews on the rating sites. Now that I know about it I’d love to try it; but I doubt it will make its way west anytime soon.
(BeerAdvocate actually also lists another beer, but it’s retired: Spiced Thanksgiving Ale from Cape Cod Beer, also in Massachusetts. But since it’s not brewed any more Mayflower gets the sole nod.)