For the peppers: Preheat a broiler. Arrange the peppers in a single layer on a heavy baking sheet. Broil, turning the peppers every 3 to 4 minutes, until charred on all sides. Place the peppers in a resealable plastic bag for 15 minutes.
Gently scrape off the burnt skin, being careful not to tear the flesh. Lay each pepper on the work surface. Using a paring knife, remove a 1/2-inch-wide strip of flesh from the side of each pepper to create an opening. Chop the strips of pepper into 1/2-inch pieces and reserve for the filling. Using a small spoon, remove the seeds from inside each pepper.
Position a rack in the center of the oven. Preheat the oven to 350 degrees F.
In a large bowl, combine the reserved chopped peppers, the corn, green onions, corn chips, chicken, basil, lime juice, salt and pepper; toss to blend. Mix in the cheese. Divide the filling among the peppers (about 2/3 cup each), packing gently and mounding at the opening. Arrange the peppers in a 13- by 9- by 2-inch baking dish. Pour the chicken broth around the peppers. Bake until peppers are heated through, 25 to 30 minutes.
For the sauce: Spoon the avocado flesh into a food processor. Add the oil, lime juice, salt and pepper. Blend until smooth.
To serve: Spoon a circle of sauce in the center of 6 plates. Place the peppers on the sauce and serve.