Ever since it was revealed that rooting the Galaxy Note 3 trips the KNOX security status and voids all warranty permanently, we've been waiting for a root exploit that wouldn't trip up KNOX, and such a root exploit is finally here. XDA developers designgears and Chainfire have released Root de la Vega, named after AT&T Mobility’s CEO Ralph de la Vega (a nice gesture that he'll likely never hear of), a method to root the Note 3 without affecting the KNOX security framework in any way.
Root de la Vega will still set the system status to unofficial and void warranty, but that can be remedied by using the Xposed Framework along with the Wanam Xposed app (Chainfire's TriangleAway app should also support this later on). The rooting process involves flashing a custom pre-rooted firmware that will wipe all data initially, but once that's done, you can do everything that you've been wanting to do on your Note 3 but haven't been able to because of Samsung's draconian security measures.
Root de la Vega is currently available for the international Snapdragon model (SM-N9005), the SM-N900W8, and for the T-Mobile, Verizon and AT&T variants. Hit up the source link for more details and to download the necessary files for achieving root access, and as always, be careful and exercise caution while attempting anything, lest you end up with a gigantic 5.7-inch paperweight.
Source: General | Verizon-specific | AT&T-specific