Whisk eggs, milk, salt, and pepper together in a bowl.

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Heat a 6-inch nonstick skillet over medium heat; pour egg mixture into the hot skillet, tilting so egg mixture covers the entire bottom of skillet. Slowly cook egg mixture until set, 5 to 10 minutes.

Arrange small dollops of cream cheese onto half the omelet; sprinkle tomato and chives over cream cheese. Fold omelet in half over the fillings. Remove skillet from heat and cover until cream cheese has softened, 2 to 3 minutes.