Prepare the chimichurri. Combine the herbs and garlic in a food processor and finely chop. Add the oil, vinegar, water, salt, pepper and hot pepper flakes and process to make a thick sauce. Correct the seasoning, adding salt or vinegar, to taste. The chimichurri should be highly seasoned. Pour a 1/4 of the chimichurri into a baking dish just large enough to hold the tenderloin.
Holding the knife parallel to the cutting board, cut the tenderloin lengthwise into 4 flat even slices. Place each slice between 2 sheets of plastic wrap and pound with the side of a cleaver (or a scaloppini pounder) to a thickness of 1/4-inch. Arrange the steaks on top of the chimichurri in the baking dish. Pour another 1/4 of the chimichurri on top. Marinate the beef for 30 minutes to 1 hour.
Set up the grill for direct grilling and preheat to high. If using charcoal, toss the chips directly on the coals. If using gas, place them in the smoker box and preheat until you see smoke. If your grill lacks a smoker box, use a foil smoking pouch. Arrange the beef slices on the grate on the diagonal and grill until cooked to taste, about 2 minutes a side for medium-rare, rotating the slices 90 degrees after 1 minute to create an attractive crosshatch of grill marks. Transfer the churrasco to plates or a platter and serve with the remaining chimichurri sauce on the side.