Crack the eggs into a small bowl and whisk vigorously until frothy and uniform. Season with a pinch of salt and pepper.
Heat an 8-inch nonstick skillet over medium-high heat. Add the butter and swirl until melted and foamy but not browned.
Pour the eggs into the skillet and let them set for about 10 seconds. Using a rubber spatula, stir the eggs in a circular motion while shaking the pan, until they are just set but still soft and creamy (about 30 seconds).
Smooth the eggs into an even layer. If using chives, sprinkle them over the eggs. Let cook undisturbed for 10 seconds until the bottom is lightly golden but the top is still moist.
Tilt the pan and use the spatula to fold the omelette in thirds, rolling it onto a plate. Serve immediately.
Tips
For a classic French omelette, the interior should be soft and slightly runny; cook longer if you prefer a firmer texture.
Add fillings like cheese, ham, or mushrooms after smoothing the eggs, before folding.