Place all the ingredients in a food processor and process, scraping the sides from time to time, until the consistency of a purée is reached, about 1 minute.
½ lb pitted black olives, 2 anchovy fillets, 1 garlic clove, 2 tablespoon capers, 3 fresh basil leaves, 1 tablespoon lemon juice, 2 tablespoon extra-virgin olive oil