Mix eggs with white and brown sugar. Add oil, mashed bananas, sour cream, vanilla and rum and mix some more.
Add flour and baking powder and mix just until incorporated (do not overmix).
Gently fold in chocolate chips With a spoon or spatula.
Transfer to a loaf pan lined with baking paper. Bake in 350 F (175 C) preheated oven until a toothpick inserted in the middle of the bread comes out clean, about 50-60 minutes.