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
Via XDA