One MS Office look alike Android based app I have used is WPS Office, since newer versions of Chromebooks may now allow installation of Android Apps you might be able to install WPS Office..
THIS LINK discusses linking Drop box to WPS on a Chromebook
"Now that you can run Android apps on Chrome OS, the likes of WPS Office can be added to the Chrome OS arsenal of productivity apps.
Installation
The first thing you must do is install WPS Office--this can only be done on a Chromebook that supports the installation of Android apps. To find out what devices are currently supported and on which devices support is coming, check out this official list. You will also need to have the Google Play Store enabled on your device (read my article, "How to install Android apps on your supported Chromebook"). Now all you have to do is follow these steps.
Click the Chrome OS menu.
Locate and click the Play Store (beta) icon.
Search for WPS Office.
Locate and click the entry by Kingsoft Office Software.
Click INSTALL.
Allow the installation to complete.
You should see an entry for WPS Office in your Chrome OS menu. Click to open the app."WPS Office can be used OFFLINE, but be very aware, new versions of WPS are extremely heavy laden with ad pollution unless you buy it.
For more info on installing Android Apps on a Chromebook see
HEREYou can checkout WPS Office website
HEREBut be aware, it IS NOT MS OFFICE, it has limitations and less features than MS OFFICE and is a lot clunkier.