Preheat oven to 350°.
Spoon applesauce into a fine sieve over a bowl; let stand 15 minutes. Discard liquid. Scrape drained applesauce into a large bowl. Add the sugar, vanilla, eggs, and egg whites; stir well.
Lightly spoon flour into dry measuring cups, and level with a knife. Combine flour, cocoa, and salt, stirring well with a whisk. Add to applesauce mixture; stir just until moist. Fold in chips.
Spoon the batter into a 13 x 9-inch baking pan coated with cooking spray, and bake at 350° for 45 minutes. Cool on a wire rack.