Where does Chrome's Gmail Offline store its files on my Mac? I have added Gmail Offline to Chrome on OS X Mavericks. Where on my Mac are the offline files (such as attachments) and the app itself stored?

Google nor StartPage are very helpful in finding any real answers.
Gmail Offline usually stores its files under your profile path.  

You can find your profile path by typing chrome://version in the address bar, and searching for Profile Path.  

The path is usually: 


  /Users/%username%/Library/Application Support/Google/Chrome/Default/  


Alternatively, if you are logged in under the account you want to explore, the path is:


  ~/Library/Application Support/Google/Chrome/Default/


If you have a Chrome user profile other than the default one, replace Default with that profile name.  

You should then look at the "Local Storage" and "Local Extension Settings" directories under that path.