Google Chrome does not keep cookies.

The solution is to remove chrome, including it's cache and config directories. To do this type the following from the terminal.

sudo apt-get remove google-chrome-stable (beta, dev, ect) un-install chrome

rm -rf ~/.cache/google-chrome* ~/.config/google-chrome* remove the cache and config directories

this will also remove the rouge folder... ~/.config/google-chromed/ (not sure where this came from... but I had to remove it) I have a suspicion this is the culprit, however I cannot figure out where it came from or what it's purpose was.

then re-install chrome and you're set: sudo apt-get install google-chrome-stable

WARNING: It is highly recommended that you sync your browser with a google account, or at the very least you backup your preferences before you wipe away your browser like that.

Check if you have "Allow local data to be set" selected. To access the option, Preferences > Under the hood > Content settings > Cookies.

I found that the Date modified of my Chrome Cookies file is a few months behind. So I presume that this SQLite3 database may be crashed or something.

I just removed the file ~/.config/google-chrome/Default/Cookies and restarted Chrome browser. This recreated the 'Cookies' file again and now the Google Chrome does keep cookies. Also make sure that answer by jokerdino is carried out.