The initial redirect from HTTP to HTTPS is a weak spot. Most users will just type "example.com" into the address bar and an active attacker can strip HTTPS from there. There'll be no padlock icon, but how many of your users really going to notice?
No. It's not. But without clients knowing about the fact that a site should be accessed only over SSL, there is no fix. Chrome isn't the only browser to support this. AFAIK, NoScript for Firefox also adds support and once this becomes widespread, more browsers might follow.
Fixing the problem for some is certainly better than not fixing it and waiting for the perfect solution that might never appear.
See http://dev.chromium.org/sts to fix this.