Preheat the oven to 350 degrees Fahrenheit (180 degrees Celsius).
Pour the olive oil, garlic, and cayenne into a large bowl and whisk together.
Cut the pita rounds into wedges (6 wedges per pita) and put in the large bowl with the spicy oil. Stir well, making sure that the pita wedges are thoroughly coated with the oil.
Place the pita breads on a baking sheet and bake in the oven for 15 minutes, or until they are slightly crispy.
Serve the pita chips warm or cool with dips.