The Chromecast runs a modified version of Android, so of course modders are all over it like white on rice. The folks at GTVHacker already gave us a working bootloader hack and root access, not that there's much you can do with it at the moment except switch to the beta or dev channel. Unfortunately, a quick over-the-air update for the Chromecast seems to have closed this modding avenue already. One XDA-Developers member has discovered this firsthand. We're currently waiting to hear back from GTV Hacker with a confirmation.
It looks like the change wasn't intended to mess with GTV Hacker's root method, which involved loading up a custom USB boot image. The 1.1 firmware adds an image verification check (a common bootloader feature) that interrupts the exploit. The good news is that the OTA update to build 12840 is rolling out slowly. If you want to root your Chromecast, unplug it right away, and there's a pretty good chance that you won't be affected.
XDA member tchebb offers a tweak that may work to disable OTA updates for Chromecast users who are already rooted, but he can't promise that it won't brick your device just yet. And if you do, well, at least you're only down thirty-five bucks, right?
Update: it looks like at least one XDA member, ddggtff3, has a temporary solution by flashing the older recovery image. This will re-enable the root exploit, but you're still left with an outdated software build (it's reporting as version 12072).
Update #2: Here's a statement given to us by GTVHacker:
I'm at a conference on my mobile between talks and unfortunately hotel rooms. I can confirm that the last update did fix the boot loader bug we exploited last week but we're researching other avenues to exploit the device. Unfortunately the entire team is currently preparing for our Google TV Secure Boot Presentation at DEF CON 21 tomorrow and won't have time to look at the patch as well as some of the other ideas we have had till Monday.