It's a Nexus. It's got an unlockable bootloader. So it was only a matter of time before someone worked out how to plug root access and superuser into Google and LG's new baby. We've been here before, folks.
In addition to a working root method from AddictiveTips's HQRaja (via XDA), there's also now a working version of ClockworkMod custom recovery for the device. This expands upon stock recovery with a bunch of new features for advanced users.
Nexus phones are Google's developer devices, so they're supposed to be easy to crack open and fiddle with. So if you're looking to run rooted apps, or even tinker with the phone's system software, this Nexus is as good as any other. AOSP support for the Nexus 4 has yet to arrive, unfortunately, but we imagine Google will be publishing the code sooner rather than later.