If you just get upgrade/fresh install the free Mac OS X Mavericks, then you might be scratching your head on this issue.
When you attempt to enable “Calendar” for your Google account under System Preferences -> Internet Accounts, you will see a spinner and after a few minutes, it displays an error message “A secure connection couldn’t be established”.
Unfortunately no solution so far and it is quite annoying. However I found a few peoples are having the same issues and you can check these forums and see if any solution helps:
Note that some solutions proposed might work – but not completely. For example:
Use Google caldav server: This only allows you to import your Google Calendar into Mac Calendar as read only. You cannot update any Google calendar entries in your Mac or add new Google calendar events in Mac Calendar.
Meanwhile, I just have to manage my Google calendar from my iOS devices rather than Mavericks.
09/12/2013 – After several tries and checked the forum above, finally the following works for me:
Enter your username (this is the tricky part): I use my gmail username without @gmail.com, and this is the trick that you need to be aware of. Use the full google account name, if your email address is firstname.lastname@example.org, then you enter the full email address.
Enter your password and type “www.google.com” as the server name.