A recurring problem with a Gnome desktop machine that is set to automatic login, like an HTPC, is Chrome's out-of-the-box dependence on the desktop environment's keystore. There are a few workarounds.
One is to simply set the Gnome Shell keystore password to blank. Yeah. Not a great idea.
The other is to invoke Chrome with a flag that has it use its own built-in keystore.
$ google-chrome-stable --password-store=basic
To make this the default, it needs to be added to the google-chrome.desktop file under /usr/share/applications:
Exec=/usr/bin/google-chrome-stable --password-store=basic %U
This is done in the first "Exec" directive in the file (there will be at least two following).