Make chips: Preheat oven to 375ºF. Split each pita in half. Brush both sides with oil and sprinkle with cumin and salt. Cut each half into 6 wedges and spread in a single layer on 2 ungreased baking sheets. Bake for 10 minutes, turning pitas over and swapping position of pans halfway through, until pitas are crisp and golden.
Make guacamole: In a glass bowl, mash avocado with a fork until chunky. Mix in onion, jalapeño, cilantro, lime juice and tomato; season with salt and pepper. Cover with plastic wrap pressed directly onto guacamole and chill for 20 minutes. Serve with cumin chips.