In a large bowl combine chicken, mashed avocado, plain Greek yogurt, cheddar cheese, red onion, green onions, cilantro, lime juice, garlic powder, and black pepper. Mix thoroughly.
For each wrap, spread a layer of approximately two spoonfuls of the mixture on a whole wheat tortilla.
Cut into even portions and serve immediately, or wrap tightly and store in the refrigerator until serving or packing in lunch boxes.