In a food processor fitted with a metal blade, combine the chickpeas, lemon juice, tahini paste, and garlic. Process until smooth. With the machine running, add 1/4 cup olive oil, a little at a time. Season with salt and pepper.
Spoon the hummus in the center of a large platter. Drizzle the hummus with olive oil. Arrange the black olives and fresh pita bread around the hummus.