Heat the butter in a frying pan over medium-high heat. Add the mushrooms in an even layer and sprinkle with the lemon zest. Cook, undisturbed, until browned, about 2 minutes. Toss with 1/4 teaspoon salt and 3/4 teaspoon pepper and continue to cook until the mushrooms are tender but not mushy, 4 to 5 minutes. Add additional salt and pepper to taste. Transfer to a serving dish and sprinkle with the chives. Serve warm.