Step 1Heat the oven to 350 degrees.
Step 2Slice the avocado down the middle and remove the pit and skin. Fill the hollow left by the pit with the chicken. Put the 2 halves of the avocado back together.
Step 3Place the buttermilk in a shallow dish, the flour in another shallow dish and the cracker crumbs in a third dish. Carefully holding the avocado together (it's slippery), dip it first in the buttermilk then roll it in the flour to coat completely. Dip it again in the buttermilk and roll it in the cracker crumbs until completely covered.
Step 4Heat about 4 cups of oil in a deep saucepan over medium-high heat. Deep-fry the avocado until golden brown, about 2 minutes. Remove the avocado with a slotted spoon and drain on paper towels.
Step 5Place the avocado in a shallow casserole and press firmly to flatten just a little. Cover the avocado with the green chile sauce and Cheddar and Jack cheeses and place in the oven until the cheese melts, about 10 minutes.