Light a grill. In a bowl, mix the parsley, olive oil, lemon juice, garlic and crushed red pepper; season with salt and pepper.
Season the skirt steak with salt and pepper and grill over a hot fire until the meat is charred on the outside and rare within, about 2 minutes per side. Transfer to a carving board and let rest for 5 minutes. Thinly slice the steak across the grain. Serve right away, passing the chimichurri sauce at the table.