Heat a non-stick frying pan, with a base is about 20cm in diameter. Add half of the oil and a little butter. Once the butter is foaming, tip in the mushrooms. Season and then sauté for 2-3 minutes. Tip into a bowl and set aside.
Wipe out the frying pan and return to the hob. Break the eggs into a bowl and add the chives; then season and lightly beat. When the pan is hot, add the remaining oil and then a little more butter, swirling it around so that the base and sides get coated.
While the butter is still foaming, pour in the egg mixture, tilting the pan from side to side. Stir gently with a fork or wooden spatula, drawing the mixture from the sides to the centre as it sets. When the eggs have almost set, scatter over the reserved mushrooms. Tilt the pan away from you slightly and use a palette knife to fold over the omelette.