Melt chocolate and shortening together in top of a double boiler, over hot but not boiling water. Stir in sugar. Place mixture in a medium bowl; cool. Beat until blended. Add vanilla. Beat in eggs one at a time, mixing well after each addition. In another medium bowl, sift flour, baking powder and salt. Stir flour mixture into chocolate mixture. Stir in chocolate chips. Refrigerate dough several hours or overnight. To bake cookies, preheat oven to 375 degrees. Lightly grease baking sheets. Break off small pieces of chilled dough and form into 1 inch balls. Place powdered sugar in shallow bowl. Roll cookies in sugar, covering completely. Place cookies 2 inches apart on prepared baking sheets. Bake 10 minutes. Cookies will be very soft, but will become firm as they cool. Immediately place on racks to cool. May be frozen.