EDIT: Be aware, Sn0wbreeze is not an official Dev Team release, and doesn't include the standard kernel patches and the sandbox issues aren't sorted out. This means certain things could be broken on it (Safari, Cydia, etc). We still recommended you use official Dev Team releases.
Two of the most popular jailbreak tools have been updated so that users who wish to jailbreak their iOS devices on 4.3.1 can now do so. Both PwnageTool, the iPhone Dev-Team's jailbreak solution, and Sn0wbreeze, a windows jailbreak tool developed by @ih8sn0w, now have beta releases that enable a tethered jailbreak for all iOS devices (excluding the iPad 2).
Redmond Pie has already posted a tutorial on how to have a "semi-tethered" jailbreak on iOS 4.3.1 using PwnageTool. In their notes they state that the release only works with the latest version of iTunes, 10.2.1, and you'll need a Universal Ramdisk Fixer, along with PwnageTool bundles for iOS 4.3.1. They also note that baseband will not be upgraded via the jailbreak.
The latest sn0wbreeze beta has been posted to ih8snow's blog, and seems like it will do the same, except users must upgrade to stock 4.3.1 before running the software. The release notes alert users to be mindful of their baseband if they continue to rely on an unlocked iPhone.
We'd recommend sitting tight, and waiting for slightly easier, untethered solutions to emerge. We've seen images of what we believe to be an iPad 2 untethered jailbreak that could supposedly work with older devices. So if we had to guess, it won't be long until these beta, tethered solutions give way to official untethered releases. But if you're aching to have iOS 4.3.1 and want it jailbroken, you can now do so. Update at your own risk!