Sift together flour, baking powder, soda, and salt in a large mixing bowl; cut in shortening with a pastry blender until mixture resembles coarse meal.
Combine pineapple, sugar, and egg in a small mixing bowl; stir well. Add to flour mixture, stirring well.
Drop by teaspoonfuls 2 inches apart onto greased cookie sheets. Bake at 325° for 10 to 12 minutes or until lightly browned. Remove from cookie sheets, and cool on wire racks.