Tried it on the latest Chrome and SD 7.1 SP2 Rollup. 'Remember for Autologin' checkbox doesn't seem to work. Chrome's own password saving system works though.
Edit:
On the other hand, I'm not sure what the checkbox is supposed to do. It doesn't seem to do anything on any other browser I tried either (Safari, Firefox, IE).
I've been using Safari for Windows for ServiceDesk portal, based on the same WebKit that Chrome is using. Haven't seen real issues besides some layout problems and the known lack of pass-through authentication.