In large bowl, combine eggs, milk and 2 tablespoons of the chives; mix well.
Melt butter over medium heat in 10-inch skillet.
Add egg mixture. Cook and stir just until eggs begin to set. Reserve 1 tablespoon cheese; add remaining cheese to egg mixture. Cook 1 to 2 minutes until eggs are set, stirring constantly. Spoon into serving bowl; top with remaining chives and cheese.