iOS 4.3.1 was released only yesterday and a jailbreak solution for this new firmware update is already available for a variety of devices. We have already covered extensive guides on how to jailbreak iPhone 4, iPad 1G and iPod touch 4G on iOS 4.3.1 using PwnageTool.
And now, PwnageTool bundle for iPhone 3GS (for both old and new bootrom) has been released. You can use this to jailbreak iPhone 3GS on the newly released iOS 4.3.1 firmware.
And as with all the current iOS 4.3 jailbreak releases, this one too is limited to tethered boot only. You will have to use tetheredboot utility to boot your device in a jailbroken state on every reboot/restart.
The instructions for jailbreaking iPhone 3GS are similar to the ones for iPad, iPhone 4 and iPod touch 4G. Simply follow the instructions posted here, with appropriate changes for iPhone 3GS where necessary, to jailbreak iOS 4.3.1 on new and old bootrom iPhone 3GS.