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MELT butter in large ovenproof skillet on medium heat. Add eggs, 1 at a time, to skillet, leaving space between eggs; sprinkle with pepper. Cook 4 to 5 min. or until whites and yolks are set. Remove eggs from skillet; set aside.
HEAT oil in same skillet. Add tortilla chips; cook 5 to 8 min. or until golden brown, stirring frequently. Add onions; cook and stir 1 min. Add enchilada sauce and 1/2 cup cheese; mix lightly. Top with eggs and remaining cheese.
HEAT broiler. Place skillet, 6 inches from heat; broil 2 to 3 min. or until cheese is melted. Top with cilantro and avocados.