Prepare pie dough according to package directions for double crust pie. Wrap dough in plastic wrap and chill.
Preheat oven to 400 degrees F. In a medium saucepan, combine chicken, salsa, taco sauce and olives. Bring to boil, then reduce heat and simmer for 5 minutes. Remove from heat and stir in cheese. Cool slightly.
On a flour-dusted surface, roll dough 1⁄8 inch thick. Using a 3-inch round cutter, cut out 18 circles, rerolling scraps as needed. Place about 1 tablespoon chicken mixture in center of each circle. Moisten edges with water. Fold circles in half and pinch to seal. Pierce tops with fork.
Place empanadas on baking sheet. Bake for 15 minutes or until golden. Serve hot.