Break the eggs into a medium bowl. Add the chives and whisk until the eggs run from the whisk in a steady stream.
Preheat a 10-in. nonstick fry pan or omelette pan on medium heat until rim is hot to the touch. Add the butter. Swirl the butter over the bottom of the pan and allow to heat for a minute longer. Add the egg mixture. Swirl the egg mixture over the bottom of the pan.
As the egg mixture cooks and sets up, tilt the pan and with a fork, pull the edge of the omelette towards the center of the pan allowing some of the raw egg to fall in and cook. Do this around the entire omelette.
When the bottom of the omelette has set up and the top is still moist, add the asparagus onto one half of the omelette. Sprinkle the cheese over the omelette. Gently shift the pan back and forth to make sure the omelette is moving freely in the pan. Slide the omelette out of the pan onto a serving plate and folding half as you do so.