Finely dice the chorizo. Add to a non stick pan over a medium heat and cook until the oil has been released and the chorizo starts to crisp - about 3-4 minutes.
Meanwhile, crack the eggs into a bowl. Add the chives and season with salt and pepper. Stir with a fork - breaking the yolks - until combined.
When the chorizo is cooked, pour the eggs into the pan. Move the pan around so that the egg forms a thin, complete layer over the base. Sprinkle the cheese on top.
Leave to cook for 2 minutes until the bottom of the egg is cooked. Then, use a spatula to fold half of the omelette over the other. Cook for another 2 minutes. Done!