Allow the tenderloin to come to room temperature on the kitchen counter. This step is really important, so don't skip it. If you don't let the tenderloin (or any large cut of meat) come to room temperature, it won't cook evenly.
While your tenderloin is warming up, go ahead and light the grill. We are going to cook this indirectly, so pile up the coals on one of your charcoal grill or light half of the burners on your gas grill.
For seasoning, less is definitely more here. I like to season mine with some fresh ground black pepper and Kosher salt. Rub the black pepper and salt all over.
Now that the beef tenderloin has warmed to room temperature and your grill is hot, place the tenderloin over the hot part of the grill to sear. We want to sear (not burn!) all sides of the tenderloin to create a nice crust.
Once all sides are seared, insert your probe thermometer into the thickest part of the tenderloin and then move it over to the cool side of the grill.
Close the lid and leave it alone!
Maintain a grill temperature (on the cool side) of around 325 - 350. A 6 pound beef tenderloin should take a little over an hour to reach our magic temperature of 130 degrees. Don't go by time though, cook to temperature.
Once the tenderloin hits 130 degrees, remove from the grill and place on a platter.
Allow the tenderloin to rest under aluminum foil for 15 minutes before carving. Serious, let it sit! If you don't, all of those delicious juices will run out of the meat.
Remove the twine.
Carve either thick filets, or for maximum tenderness, thin slices and serve!