To make the pita chips, preheat the oven to 400 degrees F. Line a rimmed baking sheet with parchment paper and set it aside.
Brush both sides of the pita bread lightly with olive oil. Stack them on top of each other and cut them into 8 small wedges. If it is hard to cut them at the same time, you can do it in two batches.
Spread the pita wedges in an even layer on the prepared sheet pan and sprinkle them with salt. Bake for 9-10 minutes, flipping halfway through. You want them to be crispy, but they burn quickly, so keep a close eye on them as they bake. Remove them from the oven and set aside to cool for a few minutes.
Meanwhile, prepare the topping. In a medium bowl, combine chickpeas, tomatoes, cucumber, green onions, olives, parsley, lemon juice, garlic, olive oil, salt, and pepper. Stir to combine and set aside.
To make the herbed tahini sauce, place the tahini, lemon juice, garlic, parsley, water, and salt in the bowl of a food processor fitted with the blade attachment. Blend* until smooth. It should have a creamy consistency, so if needed, add more water in one-tablespoon increments.
To assemble: Spread the toasted pita chips on a large plate in an even layer. Using a slotted spoon, scoop the tomato and cucumber mixture over the pita bread. Drizzle it with the tahini sauce.
Garnish with more parsley, if desired. Serve.