Preheat oven to 400 degrees. In a small bowl, mix butter, half of the lemon juice, chopped chives, mustard, lemon peel, salt and pepper until well blended.
Line a baking sheet with foil. Rub one tablespoon of mustard-chive butter over foil. Place fillets skin side down on foil and spoon about one teaspoon of lemon juice on each fillet. Season with salt and pepper.
Top each fillet with one tablespoon of mustard-chive butter. Bake for 12 to 15 minutes.
Using a slotted spatula, place the fish fillets in the center of warm plates. Spoon the chive-butter sauce over. Serve hot.