place chickpeas, half the lemon juice, tahini, garlic, olive oil, and a few grinds of salt in a food processor. Blend until smooth. Scrape down the sides of the processor and then blend again. Taste and make adjustments to the salt, lemon, and olive oil until the flavor is correct. Blend again when done.
Toast the Pita bread until warm. Serve with sliced tomatoes, jalapenos, and olives.