It's most likely not possible until there's a "hosted atom" you connect to with your browser. ChromeOS is /just/ a web browser and won't run node, which Atom uses to do its processing.
It will depend on which node features/packages are essential, but it could probably be hacked together (possibly entirely using Atom's modular design, e.g. replace the standard file IO parts with browser-friendly ones like LocalStorage and the HTML5 File API).
@Downvoters: Please do your homework[0] before downvoting. If you genuinely think my comment deserved downvotes, at least afford me the courtesy of an explanation.