Prepare the pie dough according to the package directions for a double-crust pie. Wrap the dough in plastic wrap and chill.
Preheat the oven to 400 degrees F. In a medium saucepan, combine the chicken, salsa and olives. Bring to a boil, then reduce the heat and simmer 5 minutes. Remove from the heat and stir in the cheese. Cool slightly.
On a flour-dusted surface, roll out the dough to inch thick. Using a 3-inch-round cutter, cut out 36 circles, rerolling the scraps as needed. Place about 1 tablespoon chicken mixture in the center of each circle. Moisten the edges with water.
Fold the circles in half and pinch to seal. Pierce the tops with a fork.
Place the empanadas on a baking sheet and bake 15 minutes, or until golden. Serve hot.