Our Chrome App Extension is no longer being updated, however it is open source if you would like to contribute: https://github.com/OneSignal/OneSignal-ChromeApp-SDK

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Required for setup

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1. Import OneSignal

1.1 Download the latest OneSignal Chrome App SDK. 1.2 Copy OneSignal.js to your App/Extension project folder. 1.3 Continue to 2A if you have a Chrome App. Or continue to 2B if you have a Chrome Extension.

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2A. Add OneSignal to a Chrome App

2A.1 Open your manifest.json and add OneSignal.js before you own background.js. 
"app": {
    "background": {
      "scripts": ["OneSignal.js", "background.js"]
    }
  },
Background HTML Page If your manifest.json contains a background page instead of scripts, then add OneSignal.js to your background HTML page before your own background.js. 2A.2 In your manifest.json add the following 5 permissions to your permissions array. 
"permissions": ["gcm", "storage", "notifications", "identity", "browser"],
2A.3 Continue to step 3.

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2B. Add OneSignal to a Chrome Extension

2B.1 Open your manifest.json and add OneSignal.js before you own background.js. Create new blank background.js file if you don’t have a background script already. 
"background": {
  "persistent": false,
  "scripts": ["OneSignal.js", "background.js"]
},
2B.2 In your manifest.json, add the following permissions to your permissions array: 
"permissions": ["gcm", "storage", "notifications", "identity"],
Permission Warnings Adding some of these permissions, if they were not already present, may require users to re-allow your extension after an update. The list of new permissions that may cause this is available here. Note that in Chrome 50, there is a bug that causes the “notifications” permission to cause this warning. You can find our more about this bug here.

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3. Add Required Code

3.1 Open your background.js file and add the following line outside of any function so it runs when your app/extension is loaded. Replace appId with your OneSignal App Id, and googleProjectNumber with your own as well. 
OneSignal.init({appId: "b2f7f966-d8cc-11e4-bed1-df8f05be55ba",
                googleProjectNumber: "703322744261"});
You should be all set to go with your Chrome App or Extension app.