Melt butter in an 8" skillet over medium heat. Crack eggs gently, put in two small cups and then slide into the pan, reduce heat to medium-low. Cook while spooning butter on the eggs (about 3 minutes) until whites are set. Take out eggs and put onto a plate.
Continue to cook the butter in the pan and swirl in lemon juice. Stir together and then drizzle over eggs.
Salt and pepper and chives, if desired.
2 tbsp. unsalted butter
2 eggs, cracked into two small cups
1 tsp. fresh lemon juice
Sea salt and freshly ground black pepper