Preheat oven to 400°F (20°C). Line two baking sheets with parchment paper or a silicone baking mat.
Using kitchen shears or a knife, cut each pita into 8 wedges, then tear each at the outer fold. (You'll end up with 16 wedges total per pita.)
Arrange the wedges rough side up on the baking sheets, overlapping slightly.
Drizzle olive oil over top and brush to coat each wedge generously with olive oil. Sprinkle with za'atar seasoning, salt and pepper.
Bake for 5-8 minutes, until browned and crispy. Bake closer to 8 minutes for very crispy chips or closer to 5 for softer, chewier ones. Remove from oven and allow to cool for 5 minutes before serving. Store in an airtight container.
Notes
You may need to make them in two batches, depending on the size of your baking sheets.