Cover tray with wax paper. In medium heat-proof bowl, place chocolate chips and shortening. In separate large heat-proof bowl, put very warm water (100 to 110ºF) to 1-inch depth. Carefully place bowl with chocolate into bowl with water; water should come halfway up side of chocolate bowl. With dry rubber scraper, stir chocolate and shortening CONSTANTLY, until chocolate and shortening are melted and mixture is smooth. Do NOT get water in bowl with chocolate.*
If water cools, replace it with very warm water as directed above. Remove chocolate bowl from inside water bowl. With toothpick, one at a time, dip chilled centers into chocolate mixture; gently tap fork on edge of bowl to remove excess chocolate.** Invert coated center on prepared tray; swirl small amount of melted chocolate on top to cover toothpick marks; let stand until firm. Store candies loosely covered in cool, dry place. Coating for 3 to 4 dozen centers.
* If water or moisture gets into chocolate, it can seize and tighten. As an emergency measure, ONLY, stir in additional shortening, 1/2 teaspoonful at a time, just until chocolate is fluid again. ** If chocolate mixture cools below 84ºF, return bowl with chocolate into bowl with warm water. Chocolate is best for coating between 84 and 88 ºF.