Have a look at this link on the VideoLAN forum
http://forum.videolan.org/viewtopic.php?f=12&t=70282
Basically there is a 64 bit version but it is apparently very unstable and may not even work for some users. So what I did was installed the latest 32bit version and renamed it in my application folder to "VLC32" and then downloaded the unstable 64bit version and left the name as "VLC" in my application folder. This is because Handbrake will only be able to use the 64bit version if VLC if it is named as "VLC" in your application folder.
SO ultimately, you have the 32bit version to use to watch your movies etc as normal and the 64 version just for handbrake to use for encoding. Hope this helps out