Where does Chrome's Gmail Offline store its files on my Mac?

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.

The actual files (attachments etc.) are stored in

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

In that folder my gmail files were stored under 009/t/ and then 100 files per subfolder, numbered 00 and up. Within these "File System" folders all files are numbered in sequence by which you first viewed/downloaded them and they don't have any file endings.

I would assume that unique apps are attributed their own "File System" subfolder by sequence in which you first use them. So gmail files may not alway be in subfolder "009".