Google is working on 64-bit Chrome version for Linux.

New browser version must work with all new processors and Linux versions. The biggest part of the job done by V8 group, who is also working on javascript
engine of the browser. “The v8 team did some amazing work this quarter building
a working 64-bit port. After a handful of changes on the Chromium side, I have
had Chromium Linux building on 64-bit for the last few weeks. I
believe mmoss or tony is going to get a buildbot running, and working
on packaging.” – said Google developer McNamee in this post