Whisk the eggs, milk, dill, salt, pepper, and chives together in a bowl. Using two spoons or your fingers, separate the cream cheese into small clumps. Fold the cream cheese and salmon into the egg mixture.

Heat the oil in a medium non-stick skillet over medium-low heat. Pour the egg mixture into the skillet, and stir lightly to make sure the fillings are evenly arranged in the pan. Cook until the bottom is set, but not brown, about 2 minutes. Transfer the skillet to the oven and bake until the top is set, about 8 minutes. Remove from the oven, cover, and set aside for 5 minutes.

Invert the frittata onto a large plate. Cut into wedges and serve warm or at room temperature.

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