Chrome Not Saving Passwords on Mac

I had the same issue when my IT folks at work nuked my keychain. I uninstalled and installed chrome following the steps here.

1. Go to ~/<username>/Library folder.
2. Delete Google folder from ~/Library/Application Support.
3. Delete below folders from ~/Library/Caches
   
4. Delete ~/Library/Google folder

Make sure you’ve shut down Chrome while performing this action and then either move the folder to the trash or rename it to something like backup. Chrome and then start Chrome up again.

This will fresh start your Google Chrome.

An important addition to this comprehensive answer. This will only work if you sign out of your Google account in Chrome. I tried this method several times and it wasn't until I signed out of Chrome, then deleted all the cached items and the Google folder in the Library folder that my passwords were restored.

Also, another tip (as osx has been updated).
To view the Library folder, when in
the User folder click on -> Show View Options -> There is a check box for Show Library Folder

You can also choose to show this as a default setting if required.

I had the same issue after IT nuked my Keychains. I did not need to uninstall Chrome or delete folders manually. A variation of this answer seems to work reliably.

Essentially, it seems that it is sufficient to nuke the specific user profile, rather than the entire Chrome installation. BTW, chrome://version/ reports 59.