For Chrome 44 and higher:
Edit your Chrome shortcut and add the parameter --disable-new-avatar-menu
Restart Chrome
For Chrome 43 and lower:
You can disable this annoying button via
chrome://flags
. The option you are looking for is Enable new profile management system, reachable using this direct link:chrome://flags/#enable-new-profile-management
Disable it, then restart Google Chrome and the button will be gone.