Preheat the oven to 350 degrees F. Chill the pie dough for about 15 minutes until firm (or freeze for about 10 minutes).
Line the pie shell with parchment paper or aluminum foil. Fill with pie weights or dried beans, and bake in the preheated oven for about 15 minutes until the crust looks dry. Remove the pie weights and paper or foil, and bake for an another 5-10 minutes until lightly browned.
While the crust is baking, whisk together the eggs, cream, milk, salt and pepper. Stir in the cheese, ham and chives.
Pour the custard into the parbaked pie shell while it is still warm. Transfer the quiche to the oven and bake for 40-50 minutes, until the sides are set but the center still jiggles a bit.
Cool the quiche for at least an hour before slicing and serving. Serve slightly warm or at room temperature.