I tested it now and it works fine for me.
I installed the current version of Chrome (Version 24.0.1312.52 m) and then the Tampermonkey extension, which is apperently like Greasemonkey for Firefox. It wasn't possible to install the script directly because of the "security" settings of Chrome.
I have created another Greasemonkey (Firefox) / Tampermonkey (Chrome) script that use clipboard.js.
When you hover a code section (<pre><code>) there is a small </> sign that appears on the top right corner of the script. You click it and voilà !
The code is available on this Gist.
How to use it :
Install Greasemonkey (Firefox) / ...