Combine eggs, egg whites, chives, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a bowl, stirring with a whisk.
Heat oil in an ovenproof skillet over medium heat. Add red bell peppers, onions, garlic, and remaining salt and pepper; sauté 2 minutes. Pour egg mixture over vegetables. As mixture starts to cook, gently lift edges of frittata with a spatula, and tilt pan so uncooked portion flows underneath. Cook 2 minutes; remove from heat.
Sprinkle cheese over frittata. Broil 2 minutes or until set and lightly browned. Cut into 4 wedges.