The U.S.-bound Galaxy S4 has had little time to breath and already the device has been rooted. Unearthed by the same fellow, djrbliss over at XDA (who unlocked Motorola’s bootloaders), the exploit roots every S4 variant powered by a Snapdragon processor. Instructions have been included, with many forum users claiming success; follow them and you should have no problem rooting your device.
However, as AndroidCentral rightly cautions, there’s currently no custom recoveries or stock firmware images available just yet, so flubbing up the process could be bad news. If you’re experienced with rooting, as Android users tend to be, you should have no problem. Head on over to XDA to get a full grasp on what/how to root your fresh S4.