Preheat the oven to 350 degrees F (175 degrees C). Grease a loaf pan.
Mix flour, sugar, pudding mix, salt, and baking powder together in a bowl. Stir in bananas, 3/4 of the chocolate chips, eggs, and oil. Pour mixture into the prepared pan and sprinkle the rest of the chocolate chips on top.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour 20 minutes.