Turns out this is a known bug in WebKit, and therefore effects both Chrome and Safari (not FireFox, and I have no idea about Internet Explorer or Opera)
The relevant tracker is here: https://bugs.webkit.org/show_bug.cgi?id=32292
Coincidentally, this was resolved a few days ago, so hopefully it will be in a public release soon. Since both Chrome and Safari manage to keep most users up-to-date, I don't think it's worth building a workaround in the meantime (but if anybody does have a nice workaround, please post it here!)