Apparently the Kindle Fire won't melt Android Ice Cream Sandwich, at least that's what I took from a video showing Android 4.0 running on the Amazon tablet.
A very early version of a ROM based on CyanogenMod 9 for the Fire has been getting its tires kicked over on the XDA developers forum. Forum user Jackpotclavin released a pre-alpha of the ROM as a sort of Christmas present for the developer community, but there's no guarantee you won't want to return this gift, as the developers involved openly admit it's still a bit buggy and in need of further development.
Check out the video below to see Ice Cream Sandwich in action on the Kindle Fire. You'll notice that it pretty much wipes out all the Amazon customization and integration and isn't fully usable just yet, but promising for Android fanboys nonetheless.