Android 4.3 Root by Chainfire's SuperSU

Here's The Reason why Chainfire's SuperSU works:

 It's no surprise that Google's latest update to our favorite operating system is in instant demand amongst power users and enthusiasts. Without fail, the people eagerly installing 4.3 are frequently the same ones who consider root privileges a necessity for a good Android experience. Unfortunately, it seems a wrench has been thrown into the works when it comes to exposing ultimate access, and people are experiencing more than a few hiccups because of it.
For those who have already tried playing this game, you're probably aware that the original superuser app and it's younger replacement authored by Koush aren't exactly compatible with the latest and greatest version of Android. Fortunately, SuperSU has had some success where other tools have failed, albeit with some complications.
What's causing so much trouble for would-be rooters? As it turns out, Google has patched the primary method of imparting extra powers in Android, a change which should help prevent exploits that target root binaries. With the latest iteration of Jelly Bean, /system is now mounted with the nosuid option, and it appears there is no built-in method to otherwise grant higher privileges. "Zygote processes," which are responsible for executing apps, are now restricted from running setuid root binaries, which includes su. Chainfire's solution sidesteps this pitfall by acting as a proxy, effectively performing the intended action of other root apps on its own. As Koushik Dutta points out, this solution is a bit of a hack, but one that makes sense until another option can be found.
Unfortunately, some users are reporting Chainfire's method may not be without its problems - including complaints of 100% CPU utilization and random hangs of the SuperSU app. Complications with some apps like Titanium Backup (solved by changing your backup folder location from /storage/emulated/0/TitaniumBackup to /storage/sdcard0/TitaniumBackup, thanks to Jason Bowers), further issues with writing to /system and /data/local, and apps being granted root but not acknowledging it, are also being reported. To reduce the likelihood of such problems, it's strongly suggested that you use TWRP instead of ClockWorkMod (CWM), or uncheck the option to "disable stock recovery flash" in CWM. Also, do not use the option to "avoid system recovery," as it will definitely create issues.
Given the popularity of rooting and apps that require root, it's a safe bet that a less hacky alternative will emerge fairly soon. In the mean time, custom ROMs like CyanogenMod may resort to restoring the original functionality in code until a better option turns up. For those users who intend to stick with the stock experience, Chainfire's SuperSU for 4.3 is currently the only available option.