The answer somewhat depends. There are certain Chromebooks that can run Android apps by installing them through the Play Store. On these devices, your administrator may need to do some additional configuration in your Google Apps for Education domain to allow it. Once your Chromebook is configured, you can install the MIT AI2 Companion on it through the Play Store (version 2.48 and later should work). To connect to App Inventor, you will need to use the AI Companion option and type the 6 character code into the companion app and click the "Connect with code" button.
Note that running the companion on Chromebooks isn't officially supported (yet), but we have tested and confirmed that it works using an ASUS C740 Chromebook. There is also an issue where resizing the companion window will cause it to close. We're working to fix that.
Regards,
Evan