CKP - Keepass Integration for Chrome. This extension builds Keepass access right into my Chromebook and has no difficulty supporting Google Drive and local keyfiles.
All it takes is the extension and a quick setup to tell it where to find your Keepass database, then you're on your way. It really is as simple as that, and it's free. The extension is currently in beta, but in my testing so far it seems rock steady. If your database entries are well-named, it has no problem finding the right entry based on the webpage. As you can see above, it found my "Chase Amtrak" entry when on the Chase website. It also has an option to keep the database active in an encrypted cache for about 40 minutes so you don't keep getting prompted for your master password if you're logging into a few accounts all at once. Give the extension a shot here on the Chrome Web Store.