there are two CLs on review, which will add Polymer 1.0 to Chromium. After they land, you should be able to import Polymer 1.0 resources to your extension with "chrome://resources/polymer/v1_0/*" paths. You probably need to add "chrome://resources" to extension's manifest.
I know that File Manager App, which is a component extensions, uses Polymer from "chrome://resources" (0.5 so far), so that should work for your extension as well.
As far as I know, file manager, which is a component extension, uses Polymer (0.5 so far).