In nonstick skillet set over medium-low heat, melt butter. Add shallots and cook 1 minute. Stir in flour and cook 1 minute. Stir in milk. Bring to simmer and cook, stirring for 1 minute. Stir in cheese and cook 1 minute or until blended. Sauce will thicken as it stands.
Stir in 2 Tbsp chopped chives right before serving