I'll put this in the answer too: check at https://stackoverflow.com/network-login-help to see how stackoverflow feels about your browser settings.
I was having exactly the same problem. Here's how I fixed it:
Go to settings
Scroll down and choose to see advanced settings.
Scroll down a bit to Privacy settings and click Content Settings
Click Manage exceptions
Make sure the necessary stackexchange sites are listed
The syntax of the Hostname Pattern field uses square brackets in my view needlessly
[*.], but ho hum. You could add
[*.]stackauth.com # needed: to support autologin (broken in my Chrome)
openid.stackexchange.com # needed: this sent you the third party cookie
[*.]stackoverflow.com # my favourite
[*.]meta.stackoverflow.com # just to be super sure
[*.]stackexchange.com # for those other interesting founts of knowledge