As of now, Chosen for JQuery does not work correctly when inline styles usage is forbidden by an appropriate Content-Security-Policy.
The problem is that, when it creates the "chosen" menu in set_up_html, it uses "style" param to specify width:

JQuery supports specifying the width directly (not by CSS properties): http://api.jquery.com/width/ ; this one should solve the problem.

Unfortunately, writing front-end JS compatible across different browsers (and testing it) is not my strong side, so I'll only create this issue, and will not supply any pull request with it.