Preheat an outdoor charcoal grill or oven broiler to high.
Remove the pork from the marinade, wiping off any excess. Season both sides with a generous amount of salt and pepper. Drizzle with olive oil and place on the grill. Grill the pork on the hottest part of the barbecue for 4 minutes per side, until well charred. Allow the tenderloin to rest for about 5 minutes prior to slicing. Spoon some chimichurri over the meat, drizzle with lime juice, garnish with parsley, and serve with the remaining sauce at the table.