In a 10- to 12-inch nonstick frying pan over high heat, combine 1/2 cup broth, chicken, and potatoes. Cover and cook, stirring occasionally, until chicken is no longer pink when cut in thickest portion and potatoes are just barely tender when pierced, about 5 minutes.
Stir together remaining broth and cornstarch.
When chicken is done, stir in cornstarch mixture and bring to a boil. Remove from heat. Stir in tomatoes with juice, black beans, corn, chilies, and cilantro. Pour into a 10-inch pie dish, 9-inch square pan, or 1 1/2-quart baking dish.
Unfold 1 pastry round according to package directions. On a lightly floured board, roll into a 12-inch round for pie dish, or 1 inch larger than dish of another shape. Place over filling; fold edges under and flush with pan rim, and flute firmly against rim. Cut shapes from crust and decorate top, or make a couple of decorative slits in crust.
Bake pie in a 350° oven until filling is hot in center, about 1 hour. Lay foil over crust if it begins to overbrown. Let pie cool about 10 minutes, then spoon from dish.