A few weeks ago Chainfire released a root method for the Galaxy Note 3. The only issue with the root method is that it trips Knox. Knox is a security feature built into the Galaxy Note 3 that is supposed to make this device more friendly to the enterprise market. Knox also makes rooting and modding the Note 3 a pesky process. Knox is an efuse that will void your warranty if tripped. Service centers have been instructed to refuse repair on all devices that have the Knox efuse tripped. We know that rooting your phone and modifying your phone's os will not effect your hardware in anyway. So it really isn't fair to refuse the repair of hardware defects based on software changes.
Developer "designgears" has released his new root method "Root De La Vega" which will root your Note 3 without touching the Knox efuse leaving your warranty in tact. This uses the Chainfire exploit. It is simple to apply. All you have to do is flash the appropriate file in Odin, then reboot the device copy the contents of root de la vega to your sdcard reboot, then remove the files from the sdcard and reboot one last time. Then enjoy your rooted device and your intact warranty! This is already available for several variants SMN900T, SMN9005, SMN900T, SMN900, it looks like the Verizon variant has still not been rooted. If you have one of the variants listed above head to the source link for the download.
Update: Verizon variant ROOTED: Grab it here Verizon Note 3 Root