Step 1
In a large nonstick skillet over medium heat, melt the butter until foamy. Crack the eggs into the skillet, turn the heat to medium-low, and cook, spooning the melted butter over the top of the eggs, until the whites are just set, about 3 minutes. Using a spatula, transfer the eggs to a plate.
Step 2
Continue cooking the butter in the skillet until it’s just beginning to brown, about 2 more minutes. Add the lemon juice, swirling to combine, then drizzle the lemon-butter mixture over the eggs. Season to taste with salt and black pepper, top with chives, and serve immediately.