In a large ziplock bag, add the tenderloin and pesto. Squeeze the air out of the bag and make sure that the pesto is evenly covering the tenderloin.
Allow to marinate for 30 minutes.
Preheat a grill on HIGH.
Oil the grates and turn the heat down to medium high. Add the tenderloin to the grill and cook for 2-3 minutes per side (3 sides), turning twice.
Remove to a cutting board and allow to rest for 10 minutes, before carving into 1/3' slices. Serve with additional pesto for drizzling, if desired.