J Wynia posted a pretty good (if semi-hacky) tutorial on how to get AIR applications running in Ubuntu 64. Like every other 64 bit question aimed at Adobe, I have no idea what the status of official 64 bit support for AIR is, but hopefully this gets you part of the way there.

Related posts:

1. Installing Flex Builder Linux alpha 3 on Ubuntu 8.04 “Hardy Heron”
2. Presenting Rich Internet Applications (Ajax, WPF, Flash Platform, Apollo) at Ignite Seattle
3. Running Flash Player 10 beta and Flash Player 9 Side By Side
4. Ubuntu Really IS Easy…Sort of
5. Creating AIR Applications with Custom Chrome