The hackers at Chronic Dev have come up with an unteathered solution called greenpois0n that enables iPhone owners to jailbreak a device running iOS 4.2.1 without tethering to a computer.

Not only can you jailbreak without tethering to the computer but you can also reboot the phone without having to re-jailbreak.

The jailbreak is available for Mac, Linux, and Windows. Engadget notes that this version of Greenp0ison was "rushed," so you may want to wait a little before diving in.

We should note that Apple does not approve of Jailbreaking, and doing so may invalidate your warranty. You should also be careful of further updates from Apple after jailbreaking a phone, these will almost certainly remove any functionality associated with the jailbreak - they may also stop your phone from working (although Apple typically releases updates that merely remove the jailbreak, rather than 'bricking' the phone). Even so, you jailbreak your phone at your own risk.

You can download the zip file for your system at greenpois0n.com, but be warned that the site is extremely slow in response to all of the downloads.

[Greenp0ison and @posixninja on Twitter via Engadget]