In a medium bowl, crack the eggs and add a pinch of salt and black pepper. Whisk them together until well combined and fluffy.
Heat your non-stick skillet over medium heat. Once it's warm, add a small amount of oil or butter to coat the bottom.
Pour the whisked eggs into the skillet. Allow them to cook undisturbed for about a minute, then gently stir with a spatula to scramble.
When the eggs are nearly set, sprinkle in 1 teaspoon of chives and the shredded cheddar cheese. Stir to combine and remove from heat.
Warm the flour tortillas in the skillet for about 30 seconds on each side or until they are soft. Spoon the egg mixture into the center of each tortilla.
Fold the sides of the tortilla over the filling, then roll from the bottom up, enclosing the filling securely.
Serve your Egg Burrito warm, garnished with additional chives, and enjoy with salsa and sour cream on the side.