Summary: Yes, but …
‘Is there an x64/64-bit version of Firefox?’ I’ve been asked this question a lot lately. So is there an x64/64-bit version of Firefox available. The short answer is yes. Oh, you wanted more. Yes, but …
OK, I’ll stop teasing. Yes, there is an x64/64-bit version of Firefox, and it’s 100% official code. The ‘but’ is that it is a nightly build of version 12 (the current official release is version 9) and it’s really only suited to testing rather than daily use. Using it will be buggy and plugin support will be close to non-existent.
In other words, unless you are testing, you shouldn’t run this. If you are, you can download the nightly build from here.
But there’s another option open to you. While Firefox doesn’t yet offer an x64/64-bit version of Firefox, because the project is open source, this means that others are free to do just that.