Preheat the oven to 450 degrees F. Line a rimmed baking sheet with parchment.
Mix the cranberries, sugar and orange zest and juice in a small saucepan. Place over medium heat and cook until the cranberries soften and start to burst, 8 to 10 minutes. Set aside.
Combine the cream cheese and Gruyere in a large bowl with a wooden spoon or rubber spatula until smooth.
Place the phyllo cups on the parchment-lined baking sheet. Spoon about 1 teaspoon of the cranberry sauce into each cup. Spoon about 1 teaspoon of the cheese mixture on top of the cranberry sauce. Bake until the cups are crisp and the cheese is melted and bubbling, 10 to 12 minutes. Sprinkle with chives before serving.