Their 1Password X is excellent. I've been using it on a chromebook for a few months now. Chromebook does run linux, so it should work for you too.
I think it's basically the ideal place for 1Password to be running. It's hard for malware authors to infect the chromebook with stuff like keyloggers etc. I bought the chromebook for the sole purpose of managing financial transactions -- accessing investment/bank websites etc.
Issues I faced immediately after installing it:
* Entering username/password and choosing the "Save in 1Password" option complains about not being able to reach server.
* Clicking on the extension icon and choosing New Item only shows a spinning wheel.
I'll try again when it's officially released but thanks again.
EDIT: Sent an email to their support detailing the issues.