Let beef stand at room temperature for 30 minutes. Heat a charcoal grill to medium-high, and set up direct and indirect heat zones. Rub beef with oil; season generously with salt and pepper. Sear on all sides over direct heat until caramelized, about 5 minutes per side.
Transfer beef to indirect heat, and grill, covered, turning occasionally, until a thermometer inserted into the center registers 125 for medium-rare, 20 to 30 minutes. (Grilling time will vary depending on thickness of tenderloin.) Remove beef from grill, and brush with mint-chive butter. Let stand for 15 minutes before serving; untie.