You might want to reach out to the person who admins your Google Apps domain, and see if they've explicitly disabled Chrome signin across all organizational accounts. And if so, whether it was on purpose.
Ugh if that's the case, then egg on Google's face for showing the user "Invalid user name and password" rather than saying (before even attempting to log in) "your domain administrator has disabled this feature".
It's also worth noting that "Google Talk" is a dependency for Chrome Sync; If they disabled talk years back, then Chrome Sync will also have been disabled.
To do so, have them visit:
www.google.com/a/cpanel/<your domain>/CPanelHome?pli=1#Organization/subtab=services
...and Ctrl-F "Google Chrome Sync"