No, it is not possible by design. Chrome packaged apps run separately from the browser and have no access to browser-specific features, like tabs. The closest you can get is to open an external (not in the packaged app) URL in the browser through window.open.
However, you can kind of emulate a browser by using the webview tag. See the code of the Browser sample to learn how to do it.
You can also install an extension that talks to your packaged app using the just released messaging API. See the messaging sample to learn how - it is pretty simple as long as you know the app and the extension IDs.
Thanks! I thought it was impossible, but hoped there was a workaround.
This answer is incorrect. window.open can be used from the background page to allow a packaged app to open in a browser window.
No, it is not incorrect. Packaged apps content cannot open on browser windows. You can open a regular URL using window.open, as I mentioned in my response, but you CANNOT open your app's local content in a browser window unless you use a webview. Maybe you are thinking about the old, deprecated, package apps? (those ran on tabs, not on separate windows)
Well regardless of whether this is recommended or documented, it does work, and is indeed used by a very popular app: chrome.google.com/webstore/detail/videostream-for-google-ch/ (they needed to run in a browser tab so that they could interoperate with the google cast extension, which surfaces no API to the chrome platform, so it makes sense that they would need to run in a tab)