Is it possible to run a plugin in the Chrome sandbox

It depends on whether you are asking about NPAPI plugins or Chrome extensions?

Chrome has a separate sandbox for each running tab, but if the tab is running an NPAPI plugin, that plugin has access to the computer and can perform all operations that NPAPI plugins can do.

Chrome extensions run under the sandbox of each tab they are active in.

If a Chrome extension has a content scripts, they also run in the tab sandbox in the context of the webpage. As well, the execution environments of any content scripts and the webpages that host them are isolated from each other by means of isolated worlds.
http://code.google.com/chrome/extens...t_scripts.html

Thank you for answer. What about a webpage running java or flash - would that run as a NPAPI plugin or would it run sandboxed?

AFAIK, Java or Flash running inside a browser are both NPAPI plugins.