Bake pastry shell at 400 degrees for 5 minutes. Place chicken over bottom of shell and arrange asparagus spears over chicken. Sprinkle cheese evenly over asparagus.
Combine eggs, cream, salt and pepper; blend until light and frothy. Pour gently over all. Bake at 375 degrees for about 45 minutes, or until set and knife inserted near center comes out clean. Serves 4-6.