In a small bowl, whisk eggs, water, salt and pepper. Stir in chives.
In a small nonstick skillet, heat butter over medium-high heat. Pour in egg mixture. Mixture should set immediately at edges. As eggs set, push cooked portions toward the center, letting uncooked eggs flow underneath.
When eggs are thickened and no liquid egg remains, sprinkle cheese on one side; fold omelet in half. Cut omelet in half; slide onto plates.