Preheat oven to 350.
In a large bowl, combine flour, baking soda, salt and sugars.
Mash bananas in another bowl. Add the melted butter, vanilla and applesauce to the mashed bananas.
Pour the banana mixture into the dry ingredients and stir together, just until combined.
Fold in chocolate chips.
Pour into greased loaf pan and bake 40-50 minutes, until a toothpick inserted into the center comes out clean.