Beat eggs and cream in large bowl until frothy. Stir in half the cheeses, 1 T. chives, and the pepper.
Heat oil in 10- to 12-inch ovenproof heavy skillet over medium heat until drop of egg sizzles on contact. Pour egg mixture into skillet. Cook covered over medium heat, without stirring, until edge is set but surface is still wet, 10-12 minutes.
Sprnkle remaining cheeses evenly over frittata. Broil 6 inches from heat until cheese is melted and edge is lightly puffed, about 2 minutes. Sprinkle with 1 t. chives. Serve hot.