Preheat your smoker to 250 degrees Fahrenheit and add hickory wood chunks.
Tie the prime rib with butcher's twine between each bone.
In a food processor, combine rosemary, thyme, sage, beef rub, garlic, black pepper, kosher salt, and olive oil to make a paste. Coat the prime rib evenly with this mixture.
Place a water pan in the smoker and set a wire rack above it. Put the seasoned prime rib on the rack.
Begin basting the prime rib with melted unsalted butter every 30-40 minutes after the first 30 minutes of smoking.
Continue smoking until the internal temperature of the prime rib reaches 125 degrees Fahrenheit.
Once done, remove the prime rib from the smoker and let it rest for 25 minutes at room temperature, covered with foil.
Finally, remove the backside ribs and slice the prime rib to serve.