Pat scallops dry with paper towels. Place cheese ¡n shallow dish or resealable food-storage plastic bag. Coat scallops with cheese. Discard any remaining cheese.
Heat oil and butter in 12-inch nonstick skillet over medium-high heat. Cook half of scallops at a time in oil 3 to 6 minutes, turning once, until golden brown on outside and white and opaque inside. Sprinkle with pepper and chives.