I use 2-step verification and application-specific passwords, so it's tedious to have to sign in - each time creating a new application-specific password.
I searched around for how to fix this, but couldn't find anything on my first couple of attempts. However, I've now found a solution that works for me. I hope it works for you, too:
Create a new browser user profile
If your browser user profile is corrupted, you can create a new user profile to replace the broken one:
1) Exit Google Chrome completely.
2) Go to the Start menu > Run.
3) Enter one of the following directories in the text field, then press OK.
- Windows XP: %USERPROFILE%\Local Settings\Application Data\Google\Chrome\User Data\
- Windows Vista/ Windows 7: %LOCALAPPDATA%\Google\Chrome\User Data\
5) Try opening Google Chrome again. A new "Default" folder is automatically created as you start using the browser.
If you wish, you can transfer information from your old user profile to your new one. However, this action is not recommended, since a part of your old profile was corrupt. With that in mind, to transfer your old bookmarks, copy the "Bookmarks.bak" file from the "Backup default" folder to your new "Default" folder. Once moved, rename the file from "Bookmarks.bak" to "Bookmarks" to complete the migration.
(These instructions are copied from the Chrome help pages.)