Within a day of release, iOS 4.3.1 was jailbroken. Of course 4.3.1 isn't really a major update, it just fixes a few bugs that plagued the iDevices. This jailbreak works on all devices aside from the iPad 2.
The jailbreak comes thanks to DjayB6. You will need to download a few extra tools, and once again, we will be honest and say that the jailbreak probably isn't worth the trouble it takes to install it. Still, if you must have iOS 4.3.1 and a jailbreak, then follow this guide we wrote a while back. The process is exactly the same, but replace all instances of "4.3" with "4.3.1"
Of course make sure to backup your device. Please, read the instructions fully before you begin, as they involve downloading various tools and using a few terminal commands.
You will need the following files:
– PwnageTool 4.2 here
– iOS 4.3.1 firmware (from Apple)
– PwnageTool bundle for iOS 4.3.1 (here)
– Universal Ramdisk Maker here (install required)
– tetheredboot utility here
Other than that, your iDevice and iTunes must be up to date.
Also be warned that we did not try this method out, and are not responsible for anything going wrong. Again, we'd recommend just waiting for an official jailbreak from the Dev-Team. But if you must, the instructions are here.