Mix all the ingredients except the olive oil in the bowl of a food processor. Drizzle in the oil as the processor runs. Blend until the sauce is a smooth.
Taste and adjust the heat, salt and acid. The sauce can be made in advance and kept in the fridge for days. Any not used in the Creamy Arugula Chimichurri Salad Dressing can be used on steak, pork or other meat as a condiment.