Preheat oven to 350 degrees.
Spray 8x8 baking dish with non-stick cooking spray.
Mash bananas in a medium size bowl.
Stir in sugars, applesauce, water, and vinegar until thoroughly combined.
Stir in flour, cocoa, baking soda and salt just until combined.
Fold in 1/3 cup of chocolate chips.
Pour batter into prepared dish.
Sprinkle remaining chocolate chips on top.
Bake for 33-37 minutes or until toothpick inserted into cake comes out clean.
Let cool, slice and serve.