Preheat oven to 350 degrees F (175 degrees C).

Slice the avocado in half lengthwise and remove the pit and skin.

Fill the cavity left by the pit with the shredded cooked chicken. Put the 2 avocado halves back together.

Place buttermilk in a shallow dish.

Place flour in another shallow dish.

Crush saltine crackers into crumbs and place in a third shallow dish.

Carefully dip the assembled avocado into the buttermilk, ensuring it's well-coated.

Roll the buttermilk-coated avocado in the flour, coating completely.

Dip the floured avocado back into the buttermilk, ensuring another good coating.

Roll the avocado in the crushed saltine cracker crumbs until fully covered.

Heat approximately 4 cups of oil in a deep saucepan over medium-high heat until hot.

Carefully lower the coated avocado into the hot oil.

Deep-fry the avocado until golden brown, approximately 2 minutes.

Remove the fried avocado with a slotted spoon and place on paper towels to drain excess oil.

Place the avocado in a shallow casserole dish.

Press firmly to slightly flatten the avocado.

Cover the avocado with green chile sauce.

Sprinkle shredded Cheddar and Jack cheeses over the green chile sauce.

Place the casserole dish in the preheated oven.

Bake until the cheese is melted and bubbly, approximately 10 minutes.

Serve hot with rice and beans as a side dish.