Preheat air fryer to 390 degrees for 5 minutes.
Trim any excess fat from the chicken breast. Slice into 1-inch thick strips, then each slice into small 1-inch square chunks.
Remove and discard the seeds and ribs from the peppers, then cut into 1-inch square pieces, approximately the same size as the chicken.
Add all the ingredients (except the brown sugar) to a mixing bowl; toss to coat.
Spray the air fryer basket with cooking spray and dump the mixture into the basket, arranging in a single layer as much as you can (a little overlap is fine, but if your air fryer is very small, you might need to cook in 2 batches.)
Cook for 6 minutes, shake, then cook for another 5 minutes. The chicken should be tender and slightly charred with an internal temperature of 165F.
Sprinkle with the brown sugar while still hot and toss to dissolve.
Serve on top of cooked white rice, if desired. Or make the avocado-lime sauce by combining all the ingredients in a blender; blend until smooth and incorporated. Drizzle over the chicken and peppers.